Chance a phone has app A or app B

Question

Among phones in a region, 55\% have messaging app A installed, 40\% have app B installed, and 20\% have both. What is the probability that a randomly chosen phone has at least one of the two apps?

Accepted Answer

"At least one" means app A or app B or both. Adding 55\% and 40\% counts the phones with both apps twice. Inclusion-exclusion subtracts that overlap once: P(	ext{A or B}) = 0.55 + 0.40 - 0.20 = 0.75. So 75\% of phones have at least one app. Disjoint check: only A 0.35, only B 0.20, both 0.20, neither 0.25, which sum to 1.00. Takeaway. Union equals the sum of the parts minus the intersection, counted a single time.

Chance a phone has app A or app B

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