Find the probability.
-In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 2 are ethnic minorities. Round to the Nearest ten-thousandth.
A) 0.0028
B) 0.1990
C) 0.2156
D) 0.1929

Question

Find the probability.
-In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 2 are ethnic minorities. Round to the Nearest ten-thousandth.
A) 0.0028
B) 0.1990
C) 0.2156
D) 0.1929

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. Here, n=10 (the sample size), k=2 (the number of ethnic minorities we're looking for), and p=0.33 (the probability of picking an ethnic minority). Plugging these values into the formula gives us the probability of exactly 2 ethnic minorities in a sample of 10 Physics majors, which rounds to 0.1990.

Find the Probability. -In a Certain College, 33% of the Physics Majors Are