Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations

Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the

random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X

х

0

2 3

4 or more

Probability 0. 58

1

0. 23

0. 11

0. 05

0. 03

If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F