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Raj is taking a true-false quiz with six questions. The first five questions are each worth 1 point, and the last question is worth 2 points. For any given question, the probability that Raj will answer it correctly is 2/3 and the probability that he'll answer it incorrectly is 1/3 What is the probability that Raj will score exactly 4 points on the quiz?

 Aug 11, 2023
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There are two ways for Raj to score exactly 4 points:

He gets 3 of the first 5 questions correct and the last question incorrect.

He gets 2 of the first 5 questions correct and the last question correct.

The probability of the first case is:

(3/3)^5 * (1/3) = 243/729

The probability of the second case is:

(3/3)^4 * (2/3) = 81/729

The total probability of Raj scoring exactly 4 points is the sum of these two probabilities:

243/729 + 81/729 = 324/729 = 4/9

 Aug 11, 2023

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