Question

Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?

$\dfrac{1}{36}$

$\dfrac{7}{72}$

$\dfrac{1}{9}$

$\dfrac{5}{36}$

$\dfrac{1}{6}$

Answer: B

Concepts:dice (probability)casework

Difficulty rating: 1420

Solution:

There are $6^4$ equally likely ordered outcomes.

If exactly three dice show the same value, choose the repeated value in $6$ ways, the different value in $5$ ways, and the position of the different die in $4$ ways. This gives $6\cdot5\cdot4=120$ outcomes.

If all four dice match, there are $6$ outcomes.

The probability is $\frac{120+6}{6^4}=\frac{126}{1296}=\frac7{72}$ .

Thus, the correct answer is B .

2014 AMC 10B Problem 16

Answer: B

Difficulty rating: 1420

Solution:

Problem 16 in Other Years