POSSIBLE POINTS: 7 You play a game with a friend in which you roll a 6-sided die

Question

POSSIBLE POINTS: 7 You play a game with a friend in which you roll a 6-sided die (with faces 1 reverse when it's your friend's tum to roll their 4 times, but for now let's focus on your turn! Let X be a random variable representing the total number of dollars you win on a single turn. , 2, 3, 4, 5, 6) 4 times. Each time you roll a 1, your friend pays you $1. This will Complete the probability distribution table. (Round probabilities to 4 decimal places.) PIXI To 4 decimal places, what is the probability that you win exactly $3? To 4 decimal places, what is the probability that you win at most s3?

Explanation / Answer

In a single turn, you can win following of either amount: 0,1,2,3,4.

When X = 0 , P(No ones) = (5/6)^4

When X = 1, P(exactly one one out of 4) = 4*(1/6)*(5/6)^3.

When X = 2, P(exactly two one out of 4) = 6*(1/6)^2*(5/6)^2.

When X = 3, P(exactly three one out of 4) = 4*(1/6)^3*(5/6).

When X = 4, P(all ones) = (1/6)^4.

P(X=3) = 4(1/6)^3(5/6) = 0.0154

P(X<=3) = P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1-P(X=4) = 1-(1/6)^4 = 0.9992.

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