Answer to Question #163543 in Statistics and Probability for carla reyes

Question

a survey found that one out of Filipinos says he or she has visited a dentist in any given month. if 12 people are selected at random, find the probability that exactly five will have visited a dentist last month

Answer 1

The problem is incomplete. Let's use the following assumption: a survey found that one out of five Filipinos says he or she has visited a dentist in any given month.

$p = \frac{1}{5} = 0.2 \\ q = 1 -p = 1 -0.2 = 0.8 \\ n = 12 \\ P(X=x) = \frac{n!}{x!(n-x)!} \times p^x \times (q)^{n-x} \\ P(X=5) = \frac{12!}{5!(12-5)!} \times 0.2^5 \times (0.8)^{12-5} \\ = \frac{8 \times 9 \times 10 \times 11 \times 12}{1 \times 2 \times 3 \times 4 \times 5} \times 0.2^{5} \times 0.8^7 \\ = 0.0531$