Question

1. A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 22 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?
Probability =

2. A careless university student leaves her iClicker device behind with probability 1/4 each time she attends a class. She sets out with her iClicker device to attend 5 different classes (each class is in a different lecture theatre).

a) If she arrives home without her iClicker device (after attending 5 classes), what is the probability (to 3 significant figures) that she left it in the 5th class? Hint: This is a conditional probability! Probability =

b) If she arrives home without her iClicker device and she is sure she has the iClicker device after leaving the first class, what is the probability (to 3 SIGNIFICANT figures) that she left it in the 5th class? Hint: This is a conditional probability! Probability =

Answer 1

1. It is a binomial problem with n=28 and probability =1/2

now we have to find P(22<= x <= 28)

P(22<= x <= 28) = 28c22 * .5^28 + 28c23 * .5^28 + 28c24 * .5^28 + 28c25 * .5^28 + 28c26 * .5^28 + 28c27 * .5^28 + 28c28 * .5^28

=0.00185958

2.