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。
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