Exam 7: Probability: Living With the Odds

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 or improved? Round your answer to the nearest thousandth when necessary.

Solve the problem. -How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of digits is allowed.

Evaluate the factorial expression. - $\frac { 5 ! } { 3 ! 2 ! }$

Decide whether events A and B are overlapping or non-overlapping. -Event A is that you study at least 5 hours for your math test. Event B is that you study at most 6 hours for your math test.

Determine whether the events A and B are independent. -Event A: A couple's first child is a girl. Event B: The couple's second child is a girl

Find the expected value. -In a large casino, the house wins on one of its games with a probability of 51%. All bets in the game are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet. What is The expected value to the player of a single game?

Decide whether events A and B are overlapping or non-overlapping. -You roll a red die and a blue die. Event A is that you get a sum of 9. Event B is that you get a double.

Provide an appropriate response. -Event A is that it rains in Santa Cruz tomorrow. Event B is that rains in Paris, France tomorrow. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? C: Non-overlapping, Independent? D: Non-overlapping, Dependent?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 5.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Of the 100 people who answered "yes" to a question, 6 were male. Of the 93 people who answered "no" to the question, 11 were male. If one person is selected at random from the group, what is the Probability that the person answered "yes" or was male?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.

Find the expected value. -In a large casino, the house wins on one of its games with a probability of 51,000%. All bets are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet. If patrons bet a total of $900,000 on this game in one evening, how much should the casino expect To earn?

Solve the problem. -How many different five-card hands can be dealt from a deck that has no face cards (40 cards altogether)?

The permutation formula can be used to determine which of the following? A: The number of possible license plates made with three letters and three digits given that repetition is allowed B: The number of ways of choosing 6 CDs from 20 to bring on vacation $C$ : The number of ways of choosing a first place winner and a second place winner from 10 finalists

Solve the problem. -Find the odds against drawing a heart when a card is drawn at random from a normal deck of 52 playing cards.

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.

Solve the problem. Round your answer to 2 decimal places when necessary. -At an intersection in Normal, Illinois, there were 80 vehicle accidents with 168,207 vehicles passing through the intersection. Determine the accident rate per 1000 vehicles.

Solve the problem. Round your answer to 2 decimal places when necessary. -In a recent year, there were 60 accidents in commercial aviation among major airlines over 8.1 million departures. Find the accident rate in units of accidents per 100,000 departures.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -An IRS auditor randomly selects 3 tax returns from 50 returns of which 5 contain errors. What is the probability that she selects none of those containing errors?

Write the word or phrase that best completes each statement or answers the question. -When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the numbers on the dice is 6 or 10?