A box has the numbers 2 4 5 7 8 written down on individual s

A box has the numbers {2, 4, 5, 7, 8} written down on individual slips of paper. Two slips are drawn out at random.

a) List the sample space?

b) What is the probability the sum of the two numbers is divisible by 3?

c) What are the odds both numbers are prime?

a) The sample space will contain 5C2 = 10 elements

(2,4), (2,5), (2,7), (2,8), (4,5), (4,7), (4,8), (5,7), (5,8),(7,8) (assuming that the occurence of first and second number doesn\'t matter)

b) Probability that the sum of two numbers is divisible by 3

P = number of favorable outcomes/total number of outcomes

=> 6/10 = 0.6

c) Odds that both are prime

Since there are 3 prime numbers 2,5,7

Selecting two primes from 3 can be done in 3C2

Probability = 3C2/5C2 = 3/10 = 0.3