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?

2.A brand of low-grade lightbulbs advertises that the bulbs produce 1600 lumens, but the proportion that reach this level of brightness is only 0.25. Being a miserly sort, this is the only brand I will buy. Call it a success if a lightbulb produces the advertised 1600 lumens. Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation. Hint: Try manipulating a geometric series.?

Answer 1