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问题如下：

Question An analyst determines that 60% of all US pension funds hold hedge funds. In evaluating this probability, a random sample of 10 US pension funds is taken. Using the binomial probability function, the probability that exactly 6 of the 10 firms in the sample hold hedge funds is closest to:

选项：

A.60.0%. B.11.2%. C.25.1%.

解释：

Solution

C is correct. The number of trials is 10 (n), the number of successes is 6 (x), and the probability of success is 0.60 (p). By using the formula:

$P\left(X=x\right)=\frac{n!}{\left(n?x\right)!x!}{p}^x{\left(1?p\right)}^{n?x}$

and the values given,

$P\left(X=6\right)=\frac{10!}{\left(10?6\right)!6!}{\left(0.6\right)}^6{\left(0.4\right)}^4=25.08\%$

A is incorrect. It is the given chance of success, 60%.

B is incorrect. It uses a probability of 0.40 instead than 0.60:

$\frac{10!}{\left(10?6\right)!6!}{0.4}^6{\left(1?0.4\right)}^{10?6}?11.15\%$