Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 2. The Powerball lottery is based on a random drawing of six balls from two machines. One machine contains 69 white balls (labeled 1 through 69) and the other machine contains 26 red balls (labeled 1 through 26). To determine the winning numbers, the gamemaster draws five white balls from the first machine and one red ball (the "Powerball") from the second machine (assume all outcomes are equally likely). A player in the Powerball lottery picks five different numbers between 1 and 69 (inclusive) and a sixth number between 1 and 26 (inclusive), which may duplicate one of the first five numbers. 2.1 A player wins the jackpot ($98 million) if the first five numbers picked match the numbers on the five white balls (in any order) and the sixth number picked matches the number on the red ball. What is the probability that a player wins the jackpot? 2.2 What is the probability that a player wins $100 by matching exactly four of the first five numbers (in any order), but not the sixth number? 2.3 What is the probability that a player wins $4 by matching the sixth number and at most one of the first five numbers?

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Carl Catcher has a batting average of .370, meaning that he makes a hit 37% of the times he is up at bat.  Pete Pitcher has a batting averager of only .110. Let x be the number of times Carol comes up to bat and let y be the number of times Pete comes to bat. a. If Carl bats 7 times and Pete bats 3 times, what should ther overall batting average be? b. If a total of 50 times at bat, how many times may Pete bat in order for their combined average to be as close as possible to .300? (define 3 variables, write system and solve)

In a group of friends, 1/2 liked to play football and 3/4 liked tennis. If 35 friends in the group liked both tennis and football, how many liked tennis only?

Answer d

A certain basketball team makes 70% of its free throws on average. In a game where the team shoots 40 free throws. what is the approximate probabillity that the number of free throws made by the team wilbe at least 25%

I got this wrong on a quiz and not sure why it isn’t 2.

At bedtime, you read three books to your kids, Walker, Michael, and Luke. Together, they have 32 books. If you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Suppose 10% of all redeemed coupons at a supermarket are for 50% off the item purchased. A simulation is used to model a coupon randomly selected and then recorded as 50% off or not 50% off. Which simulation best models the scenario? Place 40 equally sized pieces of paper in a hat. Of the 40, 4 read "50% off" and the rest read "not 50% off ". O Place 30 equally sized pieces of paper in a hat. Of the 30, 6 read "50% off" and the rest read "not 50% off ". O Place 80 equally sized pieces of paper in a hat. Of the 80, 10 read "50% off" and the rest read "not 50% off ". O Place 50 equally sized pieces of paper in a hat. Of the 50, 10 read "50% off" and the rest read "not 50% off ".

See picture for problem.