Exam 7: Probability: Living With the Odds

Provide an appropriate response. -When a balanced die is rolled, the probability that a six will appear is $\frac { 1 } { 6 } .$ . Suppose that you have just rolled the die five times without getting a six. What is the probability that you will get a six on The next roll of the die?

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

Solve the problem. -There are 7 finalists in a singing competition. If a person guesses randomly the top three winners (in any order), what is the probability that they Will guess correctly?

Solve the problem. -How many different five-card hands can be dealt from a deck that has only clubs (13 cards altogether)?

Determine whether the events A and B are independent. -Eight friends are drawing straws. The one who picks the short straw must cook dinner for the others. Event A: The first person does not pick the short straw Event B: The second person picks the short straw

Provide an appropriate response. -Event A is that Lisa votes for Candidate A in the gubernatorial election and event B is that she votes for candidate B. Are events A and B: A: Overlapping, Independent? B: Overlapping, Dependent? $\mathrm { C } :$ Non-overlapping, Independent? D: Non-overlapping, Dependent?

Find the expected value. -You are given 12 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn). This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to You)of the game. Round to the nearest cent.

Make a probability distribution for the given set of events. -When two fair dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$ $( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$ $( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$ $( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$ $( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$ $( 6,1 ) \quad ( 6,2 ) \quad ( 6,3 ) \quad( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Find the probability distribution for the product of the two numbers that appear when two fair dice are rolled.

Solve the problem. Round your answer to 2 decimal places when necessary. -The overall U.S. death rate for 60 year-olds is approximately 12 deaths per 1000 people. Suppose that a life insurance company insures 2000 60-year-old people. The cost of the premium is $760 per Year, and the death benefit is $60,000. What is the expected profit or loss for the insurance Company?

Solve the problem. -A student is told to answer any 7 out of 10 questions on an exam. In how many different ways can he choose the 7 questions to answer?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two fair 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is greater than 10?

Evaluate the factorial expression. - $\frac { 10 ! } { 9 ! }$

Write the word or phrase that best completes each statement or answers the question. -Suppose a mathematician computed the expected winnings (to the player)of each of seven different games in a casino. What would you expect to be true for all expected winnings?

Decide whether events A and B are overlapping or non-overlapping. -A person is selected at random from a group of doctors. Event A is that the person selected is a woman. Event B is that the person selected is a surgeon.

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 sum of 3.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?

Find the indicated probability. -In a poll of registered voters shortly before a mayoral election, people were asked which candidate they were planning to vote for. The results are shown in the table. Candidate Frequency Ford 269 Anderson 342 Garcia 527 Wong 526 Find the empirical probability that a randomly selected registered voter is planning to vote for Anderson. Round your answer to the nearest thousandth when necessary.

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 either was given the allergy drug or did not improve? Round your answer to the nearest thousandth when necessary.

Use the at least once rule to find the indicated probability. -The probability of winning $20 in a particular lottery is 0.04. What is the probability that you will get at least one $20 winner if you buy 90 tickets?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A die with 12 sides is rolled. What is the probability of rolling a number less than 11?