6.3 Wrong again?

Suppose you have a faulty calculator that does not always compute the correct result.

If the probability of getting the wrong answer is p, the probability of getting the correct answer is 1 – p. We call this the complementary probability. We assume 0 < p < 1. Assuming there is no connection between the attempts, the probability of getting the wrong answer two times in a row is p², and the probability of getting the correct answer two times in a row is (1 – p)². probability$complementary

Exercise 6.3

Compute p² and (1 – p)² for p = 0, p = 0.5, and p = 1.0.

To make this analysis useful, we want the probability of failure p to be nonzero.

For n independent attempts, the probability of getting the wrong answer is pⁿ. Let’s suppose p = 0.6. We get the wrong answer 60% of the time in many attempts. We get the correct answer 40% of the time.

After 10 attempts, the...