Question

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

$\dfrac{1}{4}$

$\dfrac{3}{8}$

$\dfrac{1}{2}$

$\dfrac{2}{3}$

$\dfrac{3}{4}$

Solution:

There are $8$ equally likely outcomes if we record Keiko's coin and Ephraim's two coins.

If Keiko gets heads, Ephraim must get exactly one head; this happens in $2$ outcomes. If Keiko gets tails, Ephraim must get no heads; this happens in $1$ outcome.

So $3$ of the $8$ equally likely outcomes work.

Thus, B is the correct answer.

2000 AMC 8 Problem 21

Solution:

Problem 21 in Other Years