In a certain college, $33 \%$ of the physics majors belong to ethnic minorities. Find the probability of the event from arandom sample of 10 students who are physics majors.
-Exactly 2 belong to an ethnic minority.
A).2156
B) .1990
C) .0028
D) .1929

Question

Quizplus · Accepted Answer

The probability can be calculated using the binomial probability formula: $ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $. Here, $ n = 10 $, $ k = 2 $, and $ p = 0.33 $. Plugging in these values gives the probability of exactly 2 students belonging to an ethnic minority as approximately 0.1990.

In a Certain College 33%33 \%33% Of the Physics Majors Belong to Ethnic Minorities

In a Certain College $33 \%$ Of the Physics Majors Belong to Ethnic Minorities