Question 1012257: twenty five percent of the engineering graduates of a university received a starting salary of $50,000 or more. if three of the graduates are chosen at random,find the probability that all have a starting salary of $50,000 or more
Answer by mathmate(429)   (Show Source):
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Question:
Twenty five percent of the engineering graduates of a university received a starting salary of $50,000 or more. if three of the graduates are chosen at random,find the probability that all have a starting salary of $50,000 or more.
Solution:
Since the size of the engineering graduate population is not given, we have to assume that the population size is infinite (or else the hypergeometric distribution applies).
We therefore assume that the probability of each graduate has a probability of 25% in having a salary of $50,000 or more.
For all three to be withing the 25% category, the probabilities have to be multiplied together (multiplication), assuming a random choice of candidates and independence of the choices.
P(all three have $50000 salary or more)
= 0.25³ = 0.015625 or 1/64
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