Exam 7: Probability: Living With the Odds

Make a probability distribution for the given set of events. -When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$ $( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$ $( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$ $( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$ $( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$ $( 6,1 ) \quad ( 6,2 ) ( 6,3 ) \quad ( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction Form.

For the students at one college the expected value for "number of siblings" is 1. Which of the following statements is a reasonable conclusion?

Find the expected value. -Four cards are numbered 1 through 4. Two of these cards are chosen at random without replacement and the numbers on them are multiplied. Find the expected value of this product.

Solve the problem. -The odds on (against)your bet are 4 to 1. If you bet $26 and win, how much will you gain? Use the definition of odds in betting.

Solve the problem. -A baseball manager has 10 players of the same ability. How many 9 player starting lineups can he create?

Find the expected value. -In a large casino, the house wins on one of its games with a probability of 50.9%. All bets are 1 : 1 . If you win, you gain the amount you bet; if you lose, you lose the amount you bet. If you play 140 Games in an evening, betting $1 each time, how much should you expect to win or lose?

Make a probability distribution for the given set of events. -Suppose that you start with a normal deck of 52 cards and remove everything except the twos, threes, and fours. So you now have a deck of twelve cards consisting of four twos, four threes, and Four fours. A card is drawn at random and replaced then another card is drawn at random and Replaced. Make a probability distribution for the sum of the two numbers that are drawn.

Solve the problem. -A pizza restaurant advertises 286 different 3-topping pizzas. How many individual toppings does the restaurant use? Assume that no topping is used more than once on a pizza and that the order of The toppings on the pizza is unimportant.

Solve the problem. -There are 10 members on a board of directors. If they must form a subcommittee of 3 members, how many different subcommittees are possible?

Find the indicated probability. -The table shows the year and political party of a random sample of students from a certain college. Party Freshman Sophomore Junior Senior Independent 13 12 18 29 Democrat 20 29 12 13 Republican 12 13 20 29 Find the empirical probability that a student at the college is an Independent. Round your answer to the nearest thousandth.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of Rain on a day following a nonrainy day is 0.250. Find the probability that January 1st and January 2nd are rainy and that January 3rd and 4th are Not rainy given that December 31st was clear all day.

Find the indicated probability. -The following table show the results of a clinical trial for an allergy drug. Allergy drug Placebo Control (notreatment) 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 received no treatment or improved? Round your answer to the nearest thousandth when necessary.

Find the expected value. -The following table gives the distribution of heights for female students at one U.S. college. Height category (inches) Percentage 57-59 7.2 60-62 20.5 63-65 36.9 66-68 19.7 69-71 10.5 72 and over 5.2 Find the expected value of height for women at this college. Use the midpoint of each category, (for example use 58 for the 57-59 category). Use 74 for the 72 and over category.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Based on meteorological records, the probability that it will snow in a certain town on January 1st is 0.441. Find the probability that in a given year it will not snow on January 1st in that town.

Use the relative frequency method to estimate the probability. Round your answer to 2 decimal places when necessary. -Every week, Joe plays chess with his father. Of the last 50 games, Joe has won 60% of the games. What is the probability that Joe will win the next game?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -What is the probability that a family with three children does not have three children of the same gender? Assume boys and girls are equally likely.

Decide whether events A and B are overlapping or non-overlapping. -A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card and event B is that the card obtained is a spade.

Use the at least once rule to find the indicated probability. -An unprepared student makes random guesses on all questions of her multiple choice test. If there are 14 questions and each question has 6 possible answers, what is the probability she will answer At least one question correctly?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -What is the probability that 4 randomly selected people all have different birthdays?

Which of the following events has a probability of 0 ? A: The sun will shine all day on January 1st in Portland, Oregon B: I will win the lottery if I buy one ticket C: Tomorrow will be Monday if today is Saturday