Question

1. Suppose the number of radios in a household has a binomial distribution
with parameters n = 7, and p = 50 %.  
Find the probability of a household having:
(a) 3 or 5 radios  
(b) 3 or fewer radios  
(c) 3 or more radios  
(d) fewer than 5 radios  
(e) more than 3 radios

2. A baseball player has a lifetime batting average of 0.228. If, in a season, this player has 225 "at bats", what is the probability he gets 58 or more hits?

Probability of 58 or more hits =

3. A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 2121 times, and the man is asked to predict the outcome in advance. He gets 1515 out of 2121 correct. What is the probability that he would have done at least this well if he had no ESP? Hint: If he has no ESP, then he's just randomly guessing, right? If he is randomly guessing, what should you use as pp, the chance of success for each individual trial?
Probability of doing at least this well =

Answer 1