3 six-sided dices are rolled. What is the probability that the product is even?

MATHEXPERTISE
Oct 21, 2018

#1**+2 **

\(P[\text{product is even}]=1-P[\text{product is odd}] = 1 - P[\text{all three dice roll odd}]\)

\(P[\text{1 die rolls odd}]=\dfrac 1 2 \\ P[\text{product is odd}]=P[\text{all 3 dice roll odd}]=\left(\dfrac 1 2\right)^3 = \dfrac 1 8\\ P[\text{product is even}]=1 - \dfrac 1 8 = \dfrac 7 8\)

Rom
Oct 21, 2018