Consider three distinct numbers: x, y, and z. If x is selected randomly from the set {6, 7, 8, 9, 10} and both y and z are selected from the set {19, 20, 21, 22}, what is the probability that x and y are prime while z is not?

Answer Choices

Correct answer marked below

1/5

1/4

1/10

1/20

Correct

3/20

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Official Explanation

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The probability of x being prime is: 1/5, as the prime number in the set {6, 7, 8, 9, 10} is 7. The probability of y being prime is: 1/4, since the only prime number in the set {19, 20, 21, 22} is…

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What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.