Using at least one of three streaming services

Question

In a household survey, 40\% use service A, 35\% use service B, and 25\% use service C. For the overlaps, 20\% use A and B, 15\% use A and C, 10\% use B and C, and 5\% use all three. What is the probability that a randomly chosen household uses at least one of the three services?

Accepted Answer

Adding the three shares double counts anyone in two services and triple counts anyone in all three. Inclusion-exclusion fixes it by adding singles, subtracting pairs, and adding the triple: P(	ext{at least one}) = (0.40 + 0.35 + 0.25) - (0.20 + 0.15 + 0.10) + 0.05. Working through it, 1.00 - 0.45 + 0.05 = 0.60. So 60\% use at least one service, and 40\% use none. Takeaway. Singles up, pairs down, triple up: the alternating signs guarantee each household is counted exactly once.

Using at least one of three streaming services

Your answer

More Probability questions