4.74 What’s wrong? In each of the following scenarios, there is something wrong. Describe what is wrong and give a reason for your answer.

1. (a) If you toss a fair coin three times and get heads all three times, then the probability of getting a tail on the next toss is much greater than one-half.

2. (b) If you multiply a random variable by 10, then the mean is multiplied by 10 and the variance is multiplied by 10.

3. (c) When finding the mean of the sum of two random variables, you need to know the correlation between them.