Question 1

Solve the problem.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of Drawing a face card or a red card?

Accepted Answer

A)  $\frac { 9 } { 13 }$ 
B)  $\frac { 8 } { 13 }$ 
C)  $\frac { 19 } { 26 }$ 
D)  $\frac { 15 } { 26 }$ 
A)  $\frac { 9 } { 13 }$ 
B)  $\frac { 8 } { 13 }$ 
C)  $\frac { 19 } { 26 }$ 
D)  $\frac { 15 } { 26 }$

Question 2

Solve the problem.
-How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not Allowed?

Accepted Answer

A)  119 
B)  2520 
C)  120 
D)  16,807 
A)  119 
B)  2520 
C)  120 
D)  16,807

Question 3

Find the probability.
-  What are the odds in favor of drawing a number greater than 2 from these cards?

Accepted Answer

A)  3:2 
B)  3:5 
C)  4:5 
D)  4:1 
A)  3:2 
B)  3:5 
C)  4:5 
D)  4:1

Question 4

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.
-In how many ways can the first award be presented to Karen and the last to Lyle?

Accepted Answer

A)  360 
B)  840 
C)  24 
D)  120 
A)  360 
B)  840 
C)  24 
D)  120

Question 5

Solve the problem.
-How many ways can a committee of 5 be selected from a club with 10 members?

Accepted Answer

A)  100,000 
B)  50 
C)  252 
D)  30,240 
A)  100,000 
B)  50 
C)  252 
D)  30,240

Question 6

Find the probability
-You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing Cards. Find the probability that the first card is a king and the second card is a queen.

Accepted Answer

A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 1 } { 663 }$ 
C)  $\frac { 13 } { 102 }$ 
D)  $\frac { 4 } { 663 }$ 
A)  $\frac { 2 } { 13 }$ 
B)  $\frac { 1 } { 663 }$ 
C)  $\frac { 13 } { 102 }$ 
D)  $\frac { 4 } { 663 }$

Question 7

Solve the problem.
-If 5 apples in a barrel of 25 apples are rotten, what is the expected number of rotten apples in a Sample of 2 apples?

Accepted Answer

A)  0.63 
B)  1 
C)  0.4 
D)  0.33 
A)  0.63 
B)  1 
C)  0.4 
D)  0.33

Question 8

Answer the question.
-How would you find the empirical probability of getting a red card, if you are choosing a card From an ordinary deck of 52 cards?

Accepted Answer

A)  Choose a card from a deck of 52 cards 2 times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by 2. 
B)  The empirical probability cannot be determined. 
C)  Choose a card from a deck of 52 cards many times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by the Total number of times a card was chosen. 
D)  Choose a card from a deck of 52 cards 52 times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by 52. 
A)  Choose a card from a deck of 52 cards 2 times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by 2. 
B)  The empirical probability cannot be determined. 
C)  Choose a card from a deck of 52 cards many times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by the Total number of times a card was chosen. 
D)  Choose a card from a deck of 52 cards 52 times and then find the relative frequency of red cards. This would be done by dividing the number of times a red card has occurred by 52.

Question 9

Estimate the indicated probability.
-The table shows the number of college students who prefer a given pizza topping. $$\begin{array} { r | r r r r } 
\text { toppings } & \text { freshman } & \text { sophomore } & \text { junior } & \text { senior } \
\hline \text { cheese } & 11 & 12 & 28 & 22 \
\text { meat } & 21 & 22 & 12 & 11 \
\text { veggie } & 12 & 11 & 21 & 22
\end{array}$$ Determine the empirical probability that a student prefers cheese toppings. Round to the nearest Thousandth.

Accepted Answer

A)  0.107 
B)  0.301 
C)  0.356 
D)  0.322 
A)  0.107 
B)  0.301 
C)  0.356 
D)  0.322

Question 10

Solve the problem.
-A survey of senior citizens at a doctorʹs office shows that 57% take blood pressure-lowering Medication, 40% take cholesterol-lowering medication, and 3% take both medications. What is the Probability that a senior citizen takes either blood pressure-lowering or cholesterol-lowering Medication? Round to the nearest hundredth.

Accepted Answer

A)  0.97 
B)  0.94 
C)  0 
D)  0.20 
A)  0.97 
B)  0.94 
C)  0 
D)  0.20

Question 11

Solve the problem.
-How many four-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions Of digits are allowed?

Accepted Answer

A)  8999 
B)  9000 
C)  10,000 
D)  256 
A)  8999 
B)  9000 
C)  10,000 
D)  256

Question 12

Solve the problem.
-There are 3 cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be Selected at random with replacement. Using a tree diagram , obtain the sample space for the Experiment. List the elements that make up the sample space.

Accepted Answer

A)  $K Q , K A , Q K , Q A , A K , A Q$ 
B)  $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { Q } Q , \mathrm { Q } A , \mathrm { AQ } , \mathrm { A } \mathrm { A }$ 
C)  $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { QK } , \mathrm { Q } Q , \mathrm { Q } \mathrm { A } , \mathrm { A } \mathrm { K } , \mathrm { A } Q , \mathrm {~A} \mathrm {~A}$ 
D)  $\mathrm { K } \mathrm { KQ } , \mathrm { KAK } , \mathrm { QQQ } , \mathrm { KQ } , \mathrm { AA } \mathrm { K }$ 
A)  $K Q , K A , Q K , Q A , A K , A Q$ 
B)  $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { Q } Q , \mathrm { Q } A , \mathrm { AQ } , \mathrm { A } \mathrm { A }$ 
C)  $\mathrm { KK } , \mathrm { KQ } , \mathrm { KA } , \mathrm { QK } , \mathrm { Q } Q , \mathrm { Q } \mathrm { A } , \mathrm { A } \mathrm { K } , \mathrm { A } Q , \mathrm {~A} \mathrm {~A}$ 
D)  $\mathrm { K } \mathrm { KQ } , \mathrm { KAK } , \mathrm { QQQ } , \mathrm { KQ } , \mathrm { AA } \mathrm { K }$

Question 13

Answer the question.
-The probability of rolling an even number on a die is $\frac { 1 } { 2 }$. Does this probability mean that, if you roll the die two times, one even number will appear? If not, what does it mean?

Accepted Answer

A)  No, but if the die was rolled 10 times, 5 outcomes would be even numbers. 
B)  No, a probability of $\frac { 1 } { 2 }$ tells us nothing. 
C)  No. It means that if a die were rolled many times, about $\frac { 1 } { 2 }$ of the outcomes would be even numbers. 
D)  Yes. 
A)  No, but if the die was rolled 10 times, 5 outcomes would be even numbers. 
B)  No, a probability of $\frac { 1 } { 2 }$ tells us nothing. 
C)  No. It means that if a die were rolled many times, about $\frac { 1 } { 2 }$ of the outcomes would be even numbers. 
D)  Yes.

Question 14

Find the probability.
-A fair die is rolled. Find the probability that the number obtained is not greater than 4.

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 2 } { 3 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 2 } { 3 }$

Question 15

Solve the problem.
-If three cards are drawn without replacement from a deck, find the probability that the third card Is a heart, given that the first two cards were hearts.

Accepted Answer

A)  $\frac { 11 } { 50 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 6 } { 25 }$ 
A)  $\frac { 11 } { 50 }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 6 } { 25 }$

Question 16

Solve the problem.
-There are 3 balls in a hat; one with the number 1 on it, one with the number 2 on it, and one with The number 5 on it. You pick a ball from the hat at random and then you roll a die. Using a tree Diagram , obtain the sample space for the experiment. List the elements that make up the sample Space.

Accepted Answer

A)  $11,12,13,14,15,16,21,22,23,24,25,26,51,52,53,54,55,56$ 
B)  $1251,1252,1253,1254,1255,1256$ 
C)  $11,12,15,21,22,25,51,52,55$ 
D)  $11,12,13,14,15,16,21,22,23,24,25,26,51,52,53,54,55,56,31,41,61,32,42,6$ $2,35,45,65$ 
A)  $11,12,13,14,15,16,21,22,23,24,25,26,51,52,53,54,55,56$ 
B)  $1251,1252,1253,1254,1255,1256$ 
C)  $11,12,15,21,22,25,51,52,55$ 
D)  $11,12,13,14,15,16,21,22,23,24,25,26,51,52,53,54,55,56,31,41,61,32,42,6$ $2,35,45,65$

Question 17

Find the probability
-A family has five children. The probability of having a girl is 1/2. What is the probability of having 2 girls followed by 3 boys? Round to the nearest ten-thousandth.

Accepted Answer

A)  0.1875 
B)  0.0313 
C)  0.6252 
D)  0.3125 
A)  0.1875 
B)  0.0313 
C)  0.6252 
D)  0.3125

Question 18

Solve the problem.
-A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different License plates possible if repetition of letters and numbers is not permitted.

Accepted Answer

A)  468,140 
B)  676,000 
C)  467,980 
D)  468,000 
A)  468,140 
B)  676,000 
C)  467,980 
D)  468,000

Question 19

Find the probability.
-On a hospital floor, 16 patients have a disease with a mortality rate of 0.1. Two of them die. Round To the nearest thousandth.

Accepted Answer

A)  0.163 
B)  0.666 
C)  0.275 
D)  0.170 
A)  0.163 
B)  0.666 
C)  0.275 
D)  0.170

Question 20

Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.
-Two pair ( 2 cards of one value, 2 of another value)

Accepted Answer

A)  $\frac { 20592 } { 433115 }$ 
B)  $\frac { 22464 } { 433115 }$ 
C)  $\frac { 5148 } { 433115 }$ 
D)  $\frac { 3432 } { 433115 }$ 
A)  $\frac { 20592 } { 433115 }$ 
B)  $\frac { 22464 } { 433115 }$ 
C)  $\frac { 5148 } { 433115 }$ 
D)  $\frac { 3432 } { 433115 }$

Solve the problem. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of Drawing a face card or a red card?

Solve the problem. -How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetitions are not Allowed?

Find the probability. - What are the odds in favor of drawing a number greater than 2 from these cards?

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. -In how many ways can the first award be presented to Karen and the last to Lyle?

Solve the problem. -How many ways can a committee of 5 be selected from a club with 10 members?

Find the probability -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing Cards. Find the probability that the first card is a king and the second card is a queen.

Solve the problem. -If 5 apples in a barrel of 25 apples are rotten, what is the expected number of rotten apples in a Sample of 2 apples?

Answer the question. -How would you find the empirical probability of getting a red card, if you are choosing a card From an ordinary deck of 52 cards?

Solve the problem. -How many four-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions Of digits are allowed?

Solve the problem. -There are 3 cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be Selected at random with replacement. Using a tree diagram , obtain the sample space for the Experiment. List the elements that make up the sample space.

Answer the question. -The probability of rolling an even number on a die is $\frac { 1 } { 2 }$ . Does this probability mean that, if you roll the die two times, one even number will appear? If not, what does it mean?

Find the probability. -A fair die is rolled. Find the probability that the number obtained is not greater than 4.

Solve the problem. -If three cards are drawn without replacement from a deck, find the probability that the third card Is a heart, given that the first two cards were hearts.

Find the probability -A family has five children. The probability of having a girl is 1/2. What is the probability of having 2 girls followed by 3 boys? Round to the nearest ten-thousandth.

Solve the problem. -A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different License plates possible if repetition of letters and numbers is not permitted.

Find the probability. -On a hospital floor, 16 patients have a disease with a mortality rate of 0.1. Two of them die. Round To the nearest thousandth.

Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low. -Two pair ( 2 cards of one value, 2 of another value)

Critical Thinking Skills

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Number Theory and the Real Number System

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The Metric System

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Exam 11: Probability