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  3. A box of light bulbs contains exactly 3 light bulbs that are defective. What is

A box of light bulbs contains exactly 3 light bulbs that are defective. What is

游客2024-01-13  13
问题 A box of light bulbs contains exactly 3 light bulbs that are defective. What is the probability that a sample of light bulbs picked at random from this box will contain at least 1 defective light bulb?
(1) The light bulbs in the sample will be picked 1 at a time without replacement.
(2) The sample will contain exactly 20 light bulbs.
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案 E
解析 It is clear that neither (1) alone nor (2) alone is sufficient.
Given (1) and (2), if the box contains 22 light bulbs, then a sample of 20 light bulbs must contain at least one defective light bulb, and hence the desired probability is equal to 1. However, if the box contains 22,000 light bulbs, then it is clear that the probability that a sample of 20 light bulbs contains at least one defective light bulb is less than 1.
The correct answer is E;
both statements together are still not sufficient.
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