The CDC has determined that a person has a 90% probability of getting measles if they are exposed to someone with the disease. Suppose you live in Brooklyn and the measles outbreak has caused everyone be exposext In your tight social circle of four friends (in addition to you), what is the theoretical probability that at least one of you five individuals contracts the measles virus? Show how you know.

Step-by-step explanation:

The probability at least one contracts the virus is the opposite (1 minus) the probability that none contracts the virus.

Using binomial probability:

P = nCr pʳ (1-p) ⁿ⁻ʳ

P (none) = ₅C₀ (0.9) ⁰ (1-0.9) ⁵⁻⁰

P (none) = (0.1) ⁵

P (none) = 0.00001

P (at least one) = 1 - P (none)

P (at least one) = 1 - 0.00001

P (at least one) = 0.99999

There is a 99.999% probability that at least one of five individuals contracts the virus.