Divisible numbers

Published

November 9, 2022

Lilly needs to pick a number divisible by 3 or by 7.

She can multiply them and use 21, but she needs to pick one number that’s not larger than 20.

Assuming Lilly selects a random number between 1 and 20, what’s the probability it will be divisible by 3 or 7?

  1. The probability is 12%

  2. The probability is 35%

  3. The probability is 40%

  4. The probability is 56%

3

Let’s assume that A is the event where Lilly selects a number divisible by 3, and B is where her number is divisible by 7. We want to find the probability of A u B, which denotes the event where Lilly selects a number divisible by 3 or 7.

The numbers divisible by 3 are 3, 6, 9, 12, 15, and 18. The numbers divisible by 7 are 7 and 14. Since the intersection of these two sets is empty, we know that events A and B are mutually exclusive, therefore:

P(A u B) = P(A) + P(B) P(A u B) = 6/20 + 2/20 P(A u B) = 8/20 P(A u B) = 40%

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