ISEE Quantitative Comparisons Question 163: Answer and Explanation

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Question: 163

4. A bag contains 3 green buttons, 5 black buttons, 6 purple buttons, and 9 red buttons. Two buttons are removed randomly from the bag without replacing the first button.

  • A. The quantity in Column A is greater.
  • B. The quantity in Column B is greater.
  • C. The two quantities are equal.
  • D. The relationship cannot be determined from the information given.

Correct Answer: B

Explanation:

B

When you need two separate probabilities to occur, you multiply the distinct probabilities (taking care to ensure that the probability of the second event assumes that the first event has occurred). Thus, the probability of picking two green buttons (Column A) is . The probability of picking only one button is . This is all you need for Column B, because one button is sufficient, and the second pick doesn't matter. Column B is greater because times any value between 0 and 1 will be less than .

Use logic. You need more luck to pick two green buttons than to pick one, which means there is a greater probability of picking one.

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