Discrete 15.4 - 15.6 Worksheet 1) Consider the random experiment of tossing a coin four times. List the outcomes of the sample space and each of the following events.

2)

a. E1: Toss at least 3 heads

d. E2: Toss at most 1 heads

b. E3: Twice as many tails as heads

e. E2: Toss all tails

c. E5: Toss same number of tails as heads

f. E4: 4 tails or less

Sample Space S = {σ1, σ2, σ3, σ4, σ5}, suppose Pr(σ1) = 0.17 and Pr(σ2) = 0.23. a. If σ3, σ4, and σ5 all have the same probability, find Pr(σ3). b. If Pr(σ3) = Pr(σ4) + Pr(σ5), find Pr(σ3). c. If Pr(σ3) = Pr(σ4) + Pr(σ5), and if Pr(σ5) = 0.1 find Pr(σ4)..

3) Eight teams are entered in a soccer tournament. Teams T3, …, T7, T8 have the same probability of winning, T1 is three times as likely to win as T3, and T2 is twice as likely to win as T1. find the probability assignment for each team winning..

4) A couple is planning to have 5 children and is concerned about their gender. a. How many different 5 children outcomes for boys and girls?

b. What is the probability the couple will have exactly 2 boys?

c. What is the probability the couple will have at least 1 boy?

d. What is the probability the couple will have at most 2 girls?

5) Draw 2 card from a standard deck of 52 without replacement a. What is the probability to draw 2 of a kind? b. What is the probability to draw 2 different cards by value? c. What is the probability of 2 black cards? d. What is the probability of a red then black?

6) Draw 2 card from a standard deck of 52 with replacement. a. What is the probability to draw 2 different cards by value? b. What is the probability of 2 non-face cards? c. What is the probability of a red and black? d. What is the probability of a face card then non-face card?

7) 8 red marbles, 7 green marbles, and 5 blue marbles are in a bag and each time a marble is chosen it is replaced back in the bag for the next draw. a. Find Pr(Red then Blue) c. Find Pr(Green and Blue)

b. Find Pr(Red then Green)

8)

d. Find Pr(Red then Red)

A computer randomly generates numbers from 0 to 9,999. a. How many different numbers can the computer generate? b. What is the probability that the number has all even digits? c. What is the probability that the number has no 9’s, 6’s and 3’s? d. What is the probability that the number has no repeated digits?

9) Roll a die ten times in a row and record the number of each roll? (Binomial Formula) a. Probability of exactly 5 1’s. b. Probability of exactly 6 even numbers? c. Probability of no even numbers? 10) Draws are made at random with replacement from the box containing 12 identical COINS marked with {1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6}. (Binomial Formula) a. Probability of exactly 4 1’s after 10 draws.

b. Probability of exactly 2 evens after 5 draws.

c. Probability of exactly 8 primes after 12 draws.