Exercise 4.5

1.

Find the probability of getting 10 heads on 20 flips of a fair coin.

2.

Find the probability of 5 aces (1's) on 5 rolls of a die.

3.

Jack reports he has ESP. To prove it, he states the color (red or black) of a card drawn at random from a deck of 52 cards. He does this for 30 cards (with replacement). Suppose he is correct on 18 of the cards. He states, "See, I got more than half correct? " What do you think? One way of reasoning here is: If Jack is just guessing how odd is it that he gets 18 or more correct out of 30?; i.e., obtain the probability that $X \geq 18$ when X is bin(30,.5).

4.

Same as last problem but this time JACK gets 24 out of 30 correct.

5.

Clyde hits 70% of his free throws in basketball. Determine the probability that Clyde makes 8 out of 14 free throws.

6.

In the last problem, Clyde plays a game in which he sinks only 4 out of 17 free throws. The coach benches him the next game, saying "Clyde, you're slipping." Clyde says, "Hey, coach it's just a bad night." To which the coach says, "A pretty rare night Clyde." Who is right? Consider the probability that $X \leq 4$ when X is bin(17,.7).

7.

Obtain and comment on the distribution of a binomial probability model with n = 6 and p = .5 .

8.

Obtain and comment on the distribution of a binomial probability model with n = 6 and p = .7 .