An experiment consists of rolling a special 22-sided die. All of the numbers, 1 through 22, are equally likely. Find the probability of each event. a. A 5 rolling a number greater than 10 and even. b. B 5 rolling a prime number or a number divisible by 5. c. C 5 rolling at most an 11. d. D 5 rolling a number divisible by 2 and 3.

Below.

Step-by-step explanation:

A. There are 12 numbers greater than 10 and the even ones are 12, 14, 16, 18, 20 and 22.

So Probability = 6/22

= 3/11.

B. Prime numbers on the die are 2,3,5,7,11,13,17,19   (8) and  numbers divisible by 5 are 5, 10, 15 and 20   Total 8+4 = 12.

So Probability = 12/22

= 6/11.

C.  First 11 numbers:

So Probability = 11/22

= 1/2.

D.  Numbers divisible by 2 and 3 are  6, 12, 18.

So Probability = 3/22.