题目
The probability of rainfall in City X on any given day is 30%. The probability of rainfall on any given day is independent of whether it rains on any other day.
Quantity A
The probability of rainfall in City X on at least one day out of two days
Quantity B
The probability of no rainfall in City X on either of those two days
选项
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.
解析
两天中至少有一天下雨的概率,等于:第一天下雨的概率 + 第二天下雨的概率 − 两天都下雨的概率。
由于每天是否下雨相互独立,因此该概率为:
0.3 + 0.3 − (0.3 × 0.3) = 0.6 − 0.09 = 0.51,即 51%。
也可以用“1 − x”的方法计算:两天中至少有一天下雨的概率 = 1 − 两天都不下雨的概率(0.7²)。
因此,概率为 1 − 0.7 × 0.7 = 1 − 0.49 = 0.51,即 51%。
B项“两天都不下雨的概率”,由上述计算可得:0.7 × 0.7 = 0.49,即 49%。
因此,A项更大。