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
