What is the probability that a number between 1 and 10,000 is a multiple of 3, 7, or both?

Question

What is the probability that a randomly chosen number between 1 and 10,000 is a multiple of 3, 7, or both?

What is the formula (or TI-83 command) to find this probability?

Answer 1

Probability of a multiple of 3, P(3) = 3,333/10,000

Probability of a multiple of 7, P(7) = 1,428/10,000

Probability of a multiple of 21, P(21) = 476/10,000

You have to subtract out the multiples of 21 once because those have been counted twice- once when counting multiples of 3 and again when counting multiples of 7.

Probability of a multiple of 3 or 7, P(3 or 7) = P(3) + P(7) - P(21) = (3,333+1,428+476)/10,000 = 5,237/10,000 = 0.5237