In a bag, there are 8 green chips labeled fro… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Probability

In a bag, there are 8 green chips labeled from 1 to 8 and 8 yellow chips also labeled from 1 to 8. If two chips are drawn one after the other without replacement, what is the probability that the first chip drawn is green and the second chip is yellow, both having the same number?

Answer Choices

Correct answer marked below

\frac{1}{30}

Correct

\frac{1}{8}

\frac{1}{32}

\frac{1}{15}

\frac{1}{64}

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Explanation

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Official Explanation

Official

To solve the problem, we need to calculate the probability of two specific events happening in sequence:

Drawing a green chip first.

Drawing a yellow chip with the same number as the green chip second.

Let's break down the solution step by step.

Step 1: Probability of Drawing a Green Chip First

There are a total of 16 chips in the bag: 8 green chips and 8 yellow chips. The probability of drawing a green chip first is:

P(\text{Green first}) = \frac{\text{Number of green chips}}{\text{Total number of chips}} = \frac{8}{16} = \frac{1}{2}

Step 2: Probability of Drawing a Yellow Chip with the Same Number Second

After drawing a green chip, there are now 15 chips left in the bag. Since the green chip drawn has a specific number (let's say number

n

), there is exactly one yellow chip with the same number

n

left in the bag.…

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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.