Question

two different numbers are selected at random from {1, 2, 3, 4, 5} and multiplied together. what is the probability that the product is even?

Answer 1

Probability of an even number product as requested = 7/10 = .7 = 70%

Explanation:

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4) and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 exact digits = 1*1 = 1. Thus, 6+1 = 7 different 2-digit products result in even numbers from among 10 possible 2-digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%