ISEE Quantitative Comparisons Question 151: Answer and Explanation
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Question: 151
2. A drawer contains 4 hats: 1 red, 1 green, and 2 plaid. One hat is selected at random and replaced. Then a second hat is selected.
- 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:
The answer is B
Probability is always a fraction, 
. The probability of obtaining one plaid hat is 2 out of 4, or 
. If the hat is replaced, the probability of selecting a plaid hat on a second try is again 2 out of 4, or . When you need two events to happen, you multiply the probabilities. Thus, the probability of getting plaid hats both times is 
.
You can think about this question logically. If you win a prize for selecting a plaid hat, it is certainly easier to win the prize once than to win it twice!