Probability help help

Question

Suppose a 50-sided die was tossed. Let B be the event that the number appearing on top of the die is divisible 5 and let C be the event that the number appearing on the top of the die has a remainder of 3 after dividing by

a. Find the elements of Event B and Event C.

b. Find the probability that the number appearing on the top of the die is divisible by 5 or has a remainder of 3

after dividing by 7?

Answer 1

Sides divisible by 5: B = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50}. |B| = 10

Sides with remainder of 3 after dividing by 7: C = {10, 17, 24, 31, 38, 45}. |C| = 6

B or C = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 17, 24, 31, 38 }. |B or C| = 14

P(B or C) = 14/50

Answer 2

B : number is divisible by 5 so { 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 }

C : remainder of 3 after dividing by 7. So this is 7p+3 where p is an integer (0, 1, 2 ...)

So C = { 3, 10, 17, 24, 31, 38, 45 }

We need p (B or C). There are 10 elements in B and 7 in C. 1 common element (10) in both.

So there are 10 + 7 - 1 = 16 elements in B or C

Probability = 16 / 50 = 8 / 25 = 0.32