Answer to Question #185094 in Statistics and Probability for winter

Question

In a survey, 25% of the people interviewed said that they bought their refrigerator during the last six months. If eleven people are selected at random, find the probability that exactly six of these people bought their refrigerator during the last six months.

Answer 1

$\text {let A event the buyer has purchased a refrigerator}$

$\text{within the last six months}$

$\text{A a random event can appear with a probability of p = 0.25}$

$\text{By the condition of the problem, we chose n = 11 independent tests}$

$\text{then }A \text{ is } Bin(n,p)$

$p(A=6)= C\binom{6}{11}p^6(p-1)^{11-6}=462*0.25^6*0.75^5\approx0.0267$

Answer: 0.0267