Exercise 4.2

1.

Let X denote the number spun on a fair spinner with the numbers 1, 2, and 3 on it. Determine the probability model of X.

2.

In the last problem, suppose we spin the the spinner twice. Let S be the sum of the numbers spun. The range of S is 2, 3, 4, 5, 6. Use a tree diagram to determine the probability model of S.

3.

Repeat the last problem if the spinner is spun 3 times.

4.

Let X denote the number of aces in a 2 card hand drawn without replacement from a well shuffled standard deck 0f 52 cards. Then the range of X is {0, 1, 2}. Use a tree diagram to determine the probability model of X.

5.

Repeat the last problem under sampling with replacement.

6.

Let X denote the number of hearts in a 2 card hand drawn without replacement from a well shuffled standard deck 0f 52 cards. Then the range of X is {0, 1, 2}. Use a tree diagram to determine the probability model of X.

7.

In the urn problem (with the balls well mixed ) discussed above, let Z denote the number of red balls in the sample (without replacement) of size 3. Use a tree diagram to determine the probability model of Z. What is the range of Z? Is it discrete or continuous?