In a particular game, a six-sided fair die is tossed. If the number of spots showing is six, you win $6; if the number of spots showing is five, you win $3; if the number of spots showing is four, you win $2; and if the number of spots showing is three, you win $1. If the number of spots showing is one or two, you win nothing. You are going to play the game twice. The probability that you win something on each of the two plays of the game is:
A)1/6.
B)1/3.
C)4/9.
D)1/4.

Question

Quizplus · Accepted Answer

To win something on each of the two plays, we need to have the outcome of each roll be 3, 4, 5, or 6. The probability of winning something on any single roll is:
P(win) = P(3) + P(4) + P(5) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 = 2/3
The probability of winning something on both rolls is the product of the probabilities of winning something on each roll:
P(win twice) = P(win) × P(win) = (2/3) × (2/3) = 4/9. Therefore, the answer is C.

In a Particular Game, a Six-Sided Fair Die Is Tossed