AMC8 2000

AMC8 2000 · Q21

AMC8 2000 · Q21. It mainly tests Probability (basic).

Keiko tosses one penny and Ephraim tosses two pennies. The probability that Ephraim gets the same number of heads that Keiko gets is

惠子抛一枚硬币，以法莲抛两枚硬币。以法莲得到与惠子相同数量正面的概率是

(A) $\frac{1}{4}$ $\frac{1}{4}$

(B) $\frac{3}{8}$ $\frac{3}{8}$

(D) $\frac{2}{3}$ $\frac{2}{3}$

(E) $\frac{3}{4}$ $\frac{3}{4}$

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Make a complete list of equally likely outcomes: \[ \begin{array}{ccc} \text{Keiko} & \text{Ephraim} & \text{Same Number of Heads?} \\ H & HH & \text{No} \\ H & HT & \text{Yes} \\ H & TH & \text{Yes} \\ H & TT & \text{No} \\ T & HH & \text{No} \\ T & HT & \text{No} \\ T & TH & \text{No} \\ T & TT & \text{Yes} \end{array} \] The probability that they have the same number of heads is $\frac{3}{8}$.

答案（B）：列出所有等可能的结果： \[ \begin{array}{ccc} \text{Keiko} & \text{Ephraim} & \text{正面数量相同？} \\ H & HH & \text{否} \\ H & HT & \text{是} \\ H & TH & \text{是} \\ H & TT & \text{否} \\ T & HH & \text{否} \\ T & HT & \text{否} \\ T & TH & \text{否} \\ T & TT & \text{是} \end{array} \] 他们正面数量相同的概率是 $\frac{3}{8}$。

Topics

CP.006 Probability (basic)