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 2 or less are ethnic minorities. Round to the Nearest ten-thousandth.
A) 0.3070
B) 0.2888
C) 0.1990
D) 0.1080

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 2 or less are ethnic minorities. Round to the Nearest ten-thousandth.
A) 0.3070
B) 0.2888
C) 0.1990
D) 0.1080

Quizplus · Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (nCk) * 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 nCk is the combination of n items taken k at a time. Here, n = 10 (the number of physics majors chosen), p = 0.33 (the probability of choosing an ethnic minority), and we're looking for the probability of k being 0, 1, or 2. We calculate the probability for each of these scenarios and sum them up to find the total probability of 2 or less ethnic minorities being chosen. The calculation yields a result closest to 0.3070, making option A the correct answer.

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