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  3. Of the 700 members of a certain organization, 120 are lawyers. Two members of th

Of the 700 members of a certain organization, 120 are lawyers. Two members of th

游客2025-02-24  33
问题 Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?
选项 A、0.5
B、0.6
C、0.7
D、0.8
E、0.9
答案 C
解析 The probability that neither of the members selected will be a lawyer is equal to the fraction
the number of ways 2 members who are not lawyers can be selected
the number of ways 2 members can be selected
where the order of selection does not matter.
    Since there are 120 members who are lawyers, there must be 700 - 120, or 580 members who are not lawyers. There are 580 ways of selecting a first member who is not a lawyer and 579 ways of selecting a second member who is not a lawyer. Multiplying these two numbers gives the number of ways to select 2 members who are not lawyers. However, in the(580)(579)ways, each group of 2 members who are not lawyers is counted twice. You can see this by considering 2 members, A and B. The 2 members can be chosen in 2 ways: A first, followed by B, and B first, followed by A. To adjust for double counting, you need to divide(580)(579)by 2.
    Similarly, the number of ways 2 members can be selected from among the 700 members is(700)(699)divided by 2. Thus, the desired probability is

Since the answer choices are all tenths, you need to approximate the value of this fraction to the nearest tenth. There are several ways to do this approximation. One way is to use your calculator to convert the fraction to a decimal and round the decimal to the nearest tenth.
    Another way is to approximate the value of the fraction as follows.

    Either way, the answer choice that is closest to the value of the fraction is 0.7.
The correct answer is Choice C.
    Another approach to this problem is to consider the random selections as two separate but successive events. The probability of selecting a first member who is not a lawyer is =580/700, because there are 580 members out of the 700 members who are not lawyers. For the second selection, there are only 699 members left to select from, because one member has already been selected. If the first member selected is not a lawyer, then there are only 579 members left who are not lawyers. So the probability of selecting a second member who is not a lawyer, given the condition that the first member selected was not a lawyer, is 579/699. The probability that both members selected will not be lawyers is the product of the two probabilities, or(580/700)(579/699), which is approximated above as 0.72. The correct answer is Choice C.
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