According to government data, the probability that an adult was never in a museum is 15%. In a random survey of 10 adults, what is the probability that two or fewer were never in a museum

Answer: 0.8202

Step-by-step explanation:

Probability an adult was never in a museum = probability of success = p = 15% = 0.15

To find probability that 2 or fewer of the 10 samples selected were never in a museum is given by:

P (X=2) or P (X=1) or P (X=0).

Where

P (X=r) = nCr * p^r * q^n-r

and n=10, p = 0.15, q=0.85

When r = 2

P (X=2) = 10C2 * 0.15² * 0.85^8 = 0.2759

When r = 1

P (X=1) = 10C1 * 0.15 * 0.85^9 = 0.3474

When r = 0

P (X=0) = 10C0 * 0.15^0 * 0.85^10 = 0.1969

Hence probability of having 2 or fewer adults who never visited the museum = 0.1969 + 0.3474 + 0.2759 = 0.8202