There are 6 green chips labeled from 1 to 6 and 6 yellow chips also labeled from 1 to 6 in a box. If two chips are drawn one after the other without putting the first one back, what is the probability that the first chip drawn is green and the second chip is yellow, both having identical numbers?

Answer Choices

Correct answer marked below

\frac{1}{11}

\frac{1}{12}

\frac{1}{16}

\frac{1}{22}

Correct

\frac{1}{23}

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Problem Statement:

There are 6 green chips labeled from 1 to 6 and 6 yellow chips also labeled from 1 to 6 in a box. If two chips are drawn one after the other without putting the first one back, what is the probability that the first chip drawn is green and the second chip is yellow, both having identical numbers?

Solution:

Total Chips:

There are a total of

6 \text{ green} + 6 \text{ yellow} = 12

chips in the box.

Probability of Drawing a Green Chip First:

The probability that the first chip drawn is green is:

P(\text{Green first}) = \frac{6}{12} = \frac{1}{2}

Probability of Drawing a Yellow Chip with the Same Number Second:…

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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.