Exam 7: Probability: Living With the Odds

Determine whether the events A and B are independent. -12 jurors are selected from a pool of 20 Event A: The first person selected is a woman Event B: The second person selected is a woman

Find the expected value. -You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you)of the game.

Find the indicated probability. -Three coins are tossed 80 times and the number of heads is recorded. The results are shown in the table below. Outcome 0 heads 1 head 2 heads 3 heads Frequency 27 9 11 33 Compute the empirical probability that at most two heads occur.

A knight may win a tournament. He may also fail to win the love of his lady. Are these events overlapping? Why or why not?

Solve the problem. -How many different three-number "combinations" are possible on a combination lock having 22 numbers on its dial? Assume that no numbers repeat. (Combination locks are really permutation Locks.)

Make a probability distribution for the given set of events. -When four fair coins are tossed, sixteen equally likely outcomes are possible as shown below: H?H? H?HT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Make a probability distribution for the number of tails when four fair coins are tossed.

A fair coin is tossed 5 times. Which of the following statements is (are)true? A: The sequence HTHTH is more likely than the sequence HHHHH. B: The sequence HTHTH and the sequence HHHHH are equally likely. C: Getting 5 tails is less likely than getting 3 tails. D: Getting 5 tails and getting 3 tails are equally likely.

Solve the problem. -A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Evaluate the factorial expression. - $\frac { 9 ! } { ( 9 - 6 ) ! }$

Find the expected value. -A contractor is considering a sale that promises a profit of $39,000 with a probability of .7 or a loss (due to bad weather, strikes, and such)of $11,000 with a probability of .3. What is the expected Profit?

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 of rain on three randomly Selected consecutive days in January.

Solve the problem. -Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket.

Write the word or phrase that best completes each statement or answers the question. -For a particular game at a casino, the expected winning for the player is -$0.87. How would you interpret this statement?

Write the word or phrase that best completes each statement or answers the question. -Explain what is wrong with the statement below. It's amazing that someone won the $100,000 prize in the lottery tonight. The probability of winning $100,000 is only 0.000000512.

Use the at least once rule to find the indicated probability. -Find the probability of at least one club when you draw cards from a standard deck 17 times; assume that you replace the card each time you draw , so there are always 52 cards to draw from.

Find the expected value. -Find the expected number of girls in a family of 7.

Write the word or phrase that best completes each statement or answers the question. -A card is selected randomly from a standard deck of 52 cards. Let $\mathrm { A } = \text { event that the card is an ace. }$ Give examples of events B, C, and D such that A and B are independent, A and C are dependent and overlapping, and A and D are non-overlapping.

Solve the problem. -A shoe store carries one brand of shoe in 5 different styles, 5 sizes, and 3 colors. How many different shoes are available of this one brand?

Find the expected value. -In a game, you have a 1/43 probability of winning $82 and a 42/43 probability of losing $6. What is your expected winning?

Solve the problem. -There are 5 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?