AMC 8 1994 Problem 22

AMC8 1994 年第 22 题

概率★★★☆☆

The two wheels shown below are spun and the two resulting numbers are added. The probability that the sum is even is

如图所示，两个转盘各自旋转一次，将所得两数相加。和为偶数的概率是

A. $\dfrac{1}{6}$
B. $\dfrac{1}{4}$
C. $\dfrac{1}{3}$
D. $\dfrac{5}{12}$
E. $\dfrac{4}{9}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

An even sum occurs when an even is added to an even or an odd is added to an odd. Looking at the areas of the regions, the chance of getting an even in the first wheel is

\frac14

and the chance of getting an odd is

\frac34

. On the second wheel, the chance of getting an even is

\frac23

and an odd is

\frac13

, resulting in an answer of D.

\frac14 \cdot \frac23 + \frac34 \cdot \frac13 = \frac16 + \frac14 = \text{(D)\

\displaystyle \frac{5}{12}

$ }$

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