AMC 8 2002 Problem 21

AMC8 2002 年第 21 题

概率★★★☆☆

Harold tosses a coin four times. The probability that he gets at least as many heads as tails is

Harold 掷一枚镍币掷了四次，那么他得到正面的次数至少和反面一样多的概率是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Case 1: There are two heads and two tails. There are

\binom{4}{2} = 6

ways to choose which two tosses are heads, and the other two must be tails. Case 2: There are three heads, one tail. There are

\binom{4}{1} = 4

ways to choose which of the four tosses is a tail. Case 3: There are four heads and no tails. This can only happen 1 way. There are a total of

2^4=16

possible configurations, giving a probability of

\displaystyle \frac{6+4+1}{16} = \text{(E)}\ \frac{11}{16}

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