Question

in a particular game, a six-sided fair die is tossed. if the number of spots showing is a six, you win $6, if the number of spots showing is a five, you win $3, if the number of spots showing is 4, you win $2, and if the number of spots showing is 3, you win $1. if the number of spots showing is 1 or 2, 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: group of answer choices

Answer 1

The probability of winning something on each of the two plays of the game is 4/9.

Step-by-step explanation:

To find the probability of winning something on each of the two plays of the game, we need to consider the individual probabilities of winning on each play and multiply them together.

On the first play, the probability of winning something is the sum of the probabilities of rolling a 6, 5, 4, or 3. Since the die is fair and has 6 sides, the probability of rolling a 6 is 1/6, the probability of rolling a 5 is 1/6, the probability of rolling a 4 is 1/6, and the probability of rolling a 3 is 1/6. So the probability of winning something on the first play is 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3.

On the second play, the probability of winning something is the same as on the first play, since the die is fair and the outcomes are independent. So the probability of winning something on the second play is also 2/3.

To find the probability of winning something on each of the two plays of the game, we multiply the probabilities together. So the probability of winning something on each of the two plays is (2/3) * (2/3) = 4/9.