Question

Questions 7 &8, please.

Question 7 5 pts Step 1. Flip a fair coin. Step 2. If you got a head in step 1, flip two fair coins. If you got a tail in step 1, flip one fair coin. Given that you got only tails in step 2, what is the chance that you got tails in step 1? Round your answer to nearest .xx Question 8 5 pts Five people roll a 60-sided die which has labels 1, 2, ..., 60. What is the chance that all five people roll different numbers? Round your answer to nearest .XXX

Answer 1

Question 7-

Let X be the event that I get tail in step 1 and Y be the event that I get tails ik step 2.

P(X|Y) = P(XY)/P(Y)

P(XY) = Probability of tail in step 1 and all tails in step 2 = (0.5)(0.5) = 0.25

P(Y) = Probability of getting all tails in step 2 = (0.5)(0.5)+(0.5)(0.5)(0.5) = 0.375

Hence the required probability = 0.25/0.375 = 0.666

Hence there are 66.7% chances that I got tail in step 1 given that I got only tails in step 2.

Question 8-

Total number of possible outcomes = (60)^5

Number of cases when all 5 people roll different numbers = 60*59*58*57*56

Hence the probability = (60*59*58*57*56)/(60)^5 which is 0.8428

Hence there are 84.28% chances that all 5 people will roll different numbers.