Probability -Statistics Homework

Please show all work!!!!

1) In horse racing, a trifecta bet is one where you need to pick the first three finishers of the race in the exact order in order to win the bet and a boxed trifecta bet is one where you need to pick the first three finishers in the race in any order to win. In this year’s (2015) Kentucky Derby a total of 18 horses raced and if a person decided to make a bet on the race:

a) How many different possible trifecta bets could they have made?

b) How many different possible boxed trifecta bets could they have made?

2) Suppose that an unfair coin comes up heads 53.2% of the time. The coin is flipped a total of 19 times.

a) What is the probability that you get exactly 11 tails?

b) What is the probability that you get at most 17 heads?

3) Suppose that you are dealt a hand of 6 cards from a standard deck of 52 playing cards.

a) What is the probability that you are dealt no more than 1 spade?

b) What is the probability that you are dealt no diamonds and exactly 2 eights?

4) It is found that when a particular 4-sided die is rolled a 1 occurs 23.2% of the time, a 2 occurs 22.7% of the time, a 3 occurs 29.8% of the time, and a 4 occurs 24.3% of the time.

a) If the die is rolled 22 times, what is the probability that an even number occurs exactly 11 times?

b) What is the expected value of a single roll of the die?

5) For the die in problem #4, let the random variable X be defined as X = (the number of times that a 3 occurs). If the die is rolled a total of three times:

a) Construct a table and histogram for the probability distribution of X.

b) Find E(X).

6) In how many ways can the letters in the word PAREIASAURUS be arranged? Note: This has nothing to do with doing the problem, but a PAREIASAURUS is an extinct reptile of the late Permian period that grew to approximately 8 feet in length and lived in the area that is now South Africa.

7) Suppose that an exam has 33 questions on it and students need to answer 25 of the questions. In how many ways can this be done if exactly 5 of the first 7 questions and the last 9 questions must be answered and question #11 must not be answered because of a typo?

8) A bagel shop offers 13 varieties of bagels, 42 flavors of cream cheese, and 29 flavors of coffee. How many different orders for a bagel, cream cheese, and a coffee can a customer place?

9) A box contains 5 green, 8 red, 3 yellow, and 11 blue marbles. Four marbles are drawn from the box simultaneously.

a) What is the probability that none of the marbles are red?

b) What is the probability that all four marbles are the same color?

c) What is the probability that you get one marble of each color?

10) A legislative committee consists of 9 Democrats, 5 Republicans, and 2 Independents. A delegation of 3 is selected to attend an environmental summit.

a) How many different delegations are possible?

b) How many different delegations consist of at least 1 Republican?

11) An 8-character password consists of one number (from 1 to 9) followed by three letters (from A to Z) followed by four more numbers (from 1 to 9).

a) How many different passwords can be formed if letters and numbers can be repeated?

b) How many different passwords can be formed that have no repeated number or letters?