Find the indicated probability. -A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. $\begin{array}{c|lllllllllll} \text { Sum } & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline \text { Frequency } & 13 & 2 & 4 & 3 & 7 & 0 & 2 & 1 & 17 & 1 & 0 \end{array}$ Compute the empirical probability of getting a sum greater than $9 .$

A) $\frac { 1 } { 50 }$ B) $\frac { 19 } { 50 }$ C) $\frac { 1 } { 6 }$ D) $\frac { 9 } { 25 }$ A) $\frac { 1 } { 50 }$ B) $\frac { 19 } { 50 }$ C) $\frac { 1 } { 6 }$ D) $\frac { 9 } { 25 }$

Find the indicated probability. -The following table show the results of a clinical trial for an allergy drug. \[\begin{array} { l | c | c | c | c } & \begin{array} { c } \text { Allergy } \\ \text { drug } \end{array} & \text { Placebo } & \begin{array} { c } \text { Control } \\ \text { (no treatment) } \end{array} & \text { Total } \\ \hline \text { Improvement } & 145 & 85 & 41 & 271 \\ \text { No improvement } & 55 & 115 & 59 & 229 \\ \text { Total } & 200 & 200 & 100 & 500 \end{array}\] What is the probability that a randomly selected person was given a placebo and improved? Round your answer to the nearest thousandth when necessary.

A) 0.17 B) 0.69 C) 0.942 D) 0.772 A) 0.17 B) 0.69 C) 0.942 D) 0.772

Find the indicated probability. -You toss four coins and record the number of tails. You repeat this many times. The results are shown below. \[\begin{array} { l | r } \text { Result } & \text { Frequency } \\ \hline 0 \text { tails } & 2 \\ 1 \text { tail } & 5 \\ 2 \text { tails } & 12 \\ 3 \text { tails } & 2 \\ 4 \text { tails } & 1 \end{array}\] Find the empirical probability of getting 4 tails. Round your answer to the nearest thousandth.

A) 0.042 B) 0.048 C) 0.273 D) 0.045 A) 0.042 B) 0.048 C) 0.273 D) 0.045

Solve the problem. -The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery. Find the expected value of the winnings for a single lottery ticket. $\begin{array}{c|l} \text { Prize (dollars) } & \text { Probability } \\ \hline 5 \text { million (jackpot) } & 1 \text { in } 76,275,360 \\ 150,000 & 1 \text { in } 2,179,296 \\ 5000 & 1 \text { in } 339,002 \\ 150 & 1 \text { in } 9686 \\ 100 & 1 \text { in } 7705 \\ 5 & 1 \text { in } 220 \\ 2 & 1 \text { in } 102 \\ 1 & 1 \text { in } 62 \end{array}$

A) $- \$ 0.81$ B) $\$ 0.24$ C) $- \$ 0.72$ D) $- \$ 0.76$ A) $- \$ 0.81$ B) $\$ 0.24$ C) $- \$ 0.72$ D) $- \$ 0.76$

Solve the problem. Round your answer to 5 decimal places when necessary. -The table shows the leading causes of death for one country in a single recent year. \[\begin{array} { l | r } { \text { Cause of Death } } & \text { Deaths } \\ \hline \text { Heart Disease } & 164,850 \\ \text { Cancer } & 125,600 \\ \text { AIDS } & 75,360 \\ \text { Stroke } & 47,885 \\ \text { Pulmonary Disease } & 44,117 \\ \text { Accidents } & 32,185 \\ \text { Diabetes } & 18,997 \\ \text { Pneumonia } & 17,584 \\ \text { Kidney Disease } & 9263 \end{array}\] Assume a population of 78.5 million. What is the empirical probability of death by accident during a single year?

A) 0.000041 B) 0.0041 C) 0.00041 D) 0.32 A) 0.000041 B) 0.0041 C) 0.00041 D) 0.32

Exam 7: Probability: Living With the Odds

Which pair(s)of events is (are)independent? A and $B$ given the following: $P(A)=0.4, P(B)=0.3, P(A$ and $B)=0.16$ $C$ and $D$ given the following: $P(C)=0.4, P(D)=0.3, P(C \mid D)=0.4$

(Multiple Choice)

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(83)

Question 201

Find the indicated probability. -A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 2 4 3 7 0 2 1 17 1 0 Compute the empirical probability of getting a sum greater than $9 .$

(Multiple Choice)

5.0/5

(79)

Question 202

Event $\mathrm { A }$ is that the weather forecast predicts sun for your hometown tomorrow. Event B is that it rains tomorrow in your home town. Are events $A$ and $B$ : A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

(Multiple Choice)

4.8/5

(65)

Question 203

Solve the problem. -A committee of 17 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?

(Multiple Choice)

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(78)

Question 204

Provide an appropriate response. -Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for determining probabilities did she use?

(Multiple Choice)

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(78)

Question 205

Find the indicated probability. -The following table show the results of a clinical trial for an allergy drug. Allergy drug Placebo Control (no treatment) Total Improvement 145 85 41 271 No improvement 55 115 59 229 Total 200 200 100 500 What is the probability that a randomly selected person was given a placebo and improved? Round your answer to the nearest thousandth when necessary.

(Multiple Choice)

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(82)

Question 206

Determine whether the events A and B are independent. -Event A: It will rain today in Seattle, Washington Event B: It will rain tomorrow in Seattle, Washington

(True/False)

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(69)

Question 207

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 6 different flags available, how many possible signals can be flown?

(Multiple Choice)

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(78)

Question 208

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 22 that have no defects. What is the probability that all four of the calculators selected Are defective?

(Multiple Choice)

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(80)

Question 209

Find the indicated probability. -You toss four coins and record the number of tails. You repeat this many times. The results are shown below. Result Frequency 0 tails 2 1 tail 5 2 tails 12 3 tails 2 4 tails 1 Find the empirical probability of getting 4 tails. Round your answer to the nearest thousandth.

(Multiple Choice)

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Question 210

Evaluate the factorial expression. -18 !

(Multiple Choice)

4.7/5

(72)

Question 211

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is Made.

(Multiple Choice)

4.8/5

(80)

Question 212

Find the indicated probability. Round your answer to 6 decimal places when necessary. -The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

(Multiple Choice)

4.8/5

(72)

Question 213

Solve the problem. Round your answer to 2 decimal places when necessary. -A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

(Multiple Choice)

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(71)

Question 214

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If three fair coins are tossed, what is the probability of not tossing three heads?

(Multiple Choice)

4.8/5

(84)

Question 215

Solve the problem. -Mark can remember only the first 5 digits of his friend's phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers And if it takes him 25 seconds to try each one, how long would it take to try every possibility?

(Multiple Choice)

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(87)

Question 216

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4?

(Multiple Choice)

4.8/5

(79)

Question 217

Solve the problem. -The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery. Find the expected value of the winnings for a single lottery ticket. Prize (dollars) Probability 5 million (jackpot) 1 in 76,275,360 150,000 1 in 2,179,296 5000 1 in 339,002 150 1 in 9686 100 1 in 7705 5 1 in 220 2 1 in 102 1 1 in 62

(Multiple Choice)

4.8/5

(91)

Question 218

Evaluate the factorial expression. - $\frac { 4 ! } { 2 ! }$

(Multiple Choice)

4.8/5

(80)

Question 219

Solve the problem. Round your answer to 5 decimal places when necessary. -The table shows the leading causes of death for one country in a single recent year. Cause of Death Deaths Heart Disease 164,850 Cancer 125,600 AIDS 75,360 Stroke 47,885 Pulmonary Disease 44,117 Accidents 32,185 Diabetes 18,997 Pneumonia 17,584 Kidney Disease 9263 Assume a population of 78.5 million. What is the empirical probability of death by accident during a single year?

(Multiple Choice)

4.9/5

(85)

Question 220

Which pair(s)of events is (are)independent? A and $B$ given the following: $P(A)=0.4, P(B)=0.3, P(A$ and $B)=0.16$ $C$ and $D$ given the following: $P(C)=0.4, P(D)=0.3, P(C \mid D)=0.4$

Find the indicated probability. -A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 2 4 3 7 0 2 1 17 1 0 Compute the empirical probability of getting a sum greater than $9 .$

Event $\mathrm { A }$ is that the weather forecast predicts sun for your hometown tomorrow. Event B is that it rains tomorrow in your home town. Are events $A$ and $B$ : A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

Solve the problem. -A committee of 17 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?

Provide an appropriate response. -Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for determining probabilities did she use?

Determine whether the events A and B are independent. -Event A: It will rain today in Seattle, Washington Event B: It will rain tomorrow in Seattle, Washington

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 6 different flags available, how many possible signals can be flown?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 22 that have no defects. What is the probability that all four of the calculators selected Are defective?

Evaluate the factorial expression. -18 !

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is Made.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

Solve the problem. Round your answer to 2 decimal places when necessary. -A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If three fair coins are tossed, what is the probability of not tossing three heads?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4?

Evaluate the factorial expression. - $\frac { 4 ! } { 2 ! }$

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Exponential Astonishment

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

Exam 7: Probability: Living With the Odds

Find the indicated probability. -A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 2 4 3 7 0 2 1 17 1 0 Compute the empirical probability of getting a sum greater than 9.9 .9.

Event A\mathrm { A }A is that the weather forecast predicts sun for your hometown tomorrow. Event B is that it rains tomorrow in your home town. Are events AAA and BBB : A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

Solve the problem. -A committee of 17 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?

Provide an appropriate response. -Melissa estimates that the probability that she will marry her boyfriend is 0.6. Which method for determining probabilities did she use?

Determine whether the events A and B are independent. -Event A: It will rain today in Seattle, Washington Event B: It will rain tomorrow in Seattle, Washington

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 6 different flags available, how many possible signals can be flown?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 22 that have no defects. What is the probability that all four of the calculators selected Are defective?

Evaluate the factorial expression. -18 !

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is Made.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -The probability that a particular region in Mexico will be hit by a hurricane in any given year is 0.07. Find the probability that the region will be hit by a hurricane in 3 consecutive years.

Solve the problem. Round your answer to 2 decimal places when necessary. -A country with a population of 103 million has 19,261 traffic fatalities. Find the fatality rate in deaths per 100,000 population.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If three fair coins are tossed, what is the probability of not tossing three heads?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be 4?

Evaluate the factorial expression. - 4!2!\frac { 4 ! } { 2 ! }2!4!​

Thinking Critically

Approaches to Problem Solving

Numbers in the Real World

Managing Money

Statistical Reasoning

Putting Statistics to Work

Exponential Astonishment

Modeling Our World

Modeling With Geometry

Mathematics and the Arts

Filters

Find the indicated probability. -A pair of dice is rolled 50 times and the sum is recorded each time. The results are shown in the table. Sum 2 3 4 5 6 7 8 9 10 11 12 Frequency 13 2 4 3 7 0 2 1 17 1 0 Compute the empirical probability of getting a sum greater than $9 .$

Event $\mathrm { A }$ is that the weather forecast predicts sun for your hometown tomorrow. Event B is that it rains tomorrow in your home town. Are events $A$ and $B$ : A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

Evaluate the factorial expression. - $\frac { 4 ! } { 2 ! }$