SOLUTION: On average, Loren can answer 2/3 of the questions in an exam paper on mathematics. If the exam paper contains five questions and a minimum of three correct answers in required

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Question 367570: On average, Loren can answer 2/3 of the questions in an exam paper on mathematics.
If the exam paper contains five questions and a minimum of three correct answers in required to pass, find the probability that Loren will pass the exam.
Answer by Theo(13342) (Show Source):
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the probability that Loren will get an answer correct is 2/3.

the number of questions is 5.

the probability that she will get exactly 3 questions correct is (2/3)^3 * (1/3)^2

the probability that she will get exactly 4 questions correct is (2/3)^4 * (1/3)^1

the probability that she will get exactly 5 questions correct is (2/3)^5 * (1/3)^0

the number of ways that she can get 3 out of 5 questions correct is 5! / (2! * 3!) = 10

the number of ways that she can get 4 out of 5 questions correct is 5! / 4! * 1!) = 5

the number of ways that she can get 5 out of 5 questions correct = 1.

her total probability of getting at least 3 out of 5 questions correct is equal to:

[10 * (2/3)^3 * (1/3)^2] + [5 * (2/3)^4 * (1/3)^1] + [1 * (2/3)^5]

This is equivalent to:

.329218107 + .329218107 + .131687243 which is equal to .790123457