Question

2)

if two distinct numbers are chosen at random from this set: (1, 5, 10, 100) what is the probability that their sum will be greater than 100?

Answer 1

Answer: 0.5

Explanation:

Number of permutations (without restrictions) = 4C2 = 6

Number of ways for the sum to be greater than 100 = 3 (only when the number 100 is chosen to be 1 of the 2 numbers)

Longer approach:

1) 1 and 5 total = 6 < 100

2) 1 and 10 total = 11 < 100

3) 1 and 100 total = 101 > 100

4) 5 and 10 total = 15 < 100

5) 5 and 100 total = 105 > 100

6) 10 and 100 total = 110 > 100

Hence 3 out of the 6 combinations are greater than 100 for their sums.

Probability = 3/6 = 0.5