Having at least one of three social apps

Question

Among students, 60\% use app P, 50\% use app Q, and 30\% use app R. For overlaps, 30\% use P and Q, 25\% use P and R, 20\% use Q and R, and 10\% use all three. What is the probability that a randomly chosen student uses at least one of the three apps?

Accepted Answer

Three overlapping groups need inclusion-exclusion: add the singles, subtract all pairwise overlaps, add back the triple overlap. P(	ext{at least one}) = (0.60 + 0.50 + 0.30) - (0.30 + 0.25 + 0.20) + 0.10. That is 1.40 - 0.75 + 0.10 = 0.75. So 75\% use at least one app, and 25\% use none. Takeaway. The three-event formula is singles minus pairs plus triple, and it works no matter how heavy the overlaps are.

Having at least one of three social apps

Your answer

More Probability questions