In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority? Round to three decimal places.
A) 0.982
B) 0.913
C) 0.055
D) 0.985

Question

Quizplus · Accepted Answer

The probability that no more than 6 students belong to an ethnic minority can be calculated using the binomial probability formula. The probability of selecting a student who belongs to an ethnic minority is 0.33, and the probability of selecting a student who does not belong to an ethnic minority is 0.67. The sum of the probabilities of selecting 0 to 6 students who belong to an ethnic minority gives the total probability of no more than 6 students belonging to an ethnic minority. This calculation involves summing the binomial probabilities for 0 through 6 successes (students belonging to an ethnic minority) out of 10 trials (students selected), which results in a probability of approximately 0.982.

In a Certain College, 33% of the Physics Majors Belong