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Thirty-three percent of all students at a high school like beef stew. Out of 30 students, 40 are selected randomly and asked whether they liked beef stew. If liking beef stew is a success, what is the probability of a failure for this binomial experiment?

Thirty-three percent of all students at a high school like beef stew. Out of $30$ students, $40$ are selected randomly and asked whether they liked beef stew. If liking beef stew is a success, what is the probability of a failure for this binomial experiment?

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Experiment design

Full solution

Q. Thirty-three percent of all students at a high school like beef stew. Out of

30

students,

40

are selected randomly and asked whether they liked beef stew. If liking beef stew is a success, what is the probability of a failure for this binomial experiment?

Calculate probability: Calculate the probability of a student liking beef stew. $\newline$ Probability of liking = $33\% = 0.33$ $\newline$ Probability of not liking (failure) = $1 - 0.33 = 0.67$
Find probability of failure: Since $40$ students are selected, and the probability of not liking beef stew is $0.67$ , we use this to find the probability of a failure in this binomial experiment. $\newline$ This is a straightforward calculation of the probability of a single outcome, which is not liking beef stew.

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