Probability of rolling a sum of 9 with 2 dice, given that at least one die shows 4.

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Let A = sum = 9, B = at least one die = 4 Favorable outcomes for B: (4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(1,4),(2,4),(3,4),(5,4),(6,4) 11 outcomes Outcomes where sum = 9 and at least one die = 4: (4,5),(5,4) 2 outcomes P(A|B) = 2 / 11

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Asked 12 days ago|2/23/2026 9:25:27 AM

Updated 12 days ago|2/23/2026 9:53:32 AM

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cruz30

Let A = sum = 9, B = at least one die = 4

Favorable outcomes for B: (4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(1,4),(2,4),(3,4),(5,4),(6,4) 11 outcomes
Outcomes where sum = 9 and at least one die = 4: (4,5),(5,4) 2 outcomes
P(A|B) = 2 / 11

Added 12 days ago|2/23/2026 9:52:46 AM

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Salas1987

The total number of possible outcomes: 6 * 6 = 36.

P(A and B) = Number of outcomes in (A and B) / Total outcomes = 2 / 36.

P(B) = Number of outcomes in B / Total outcomes = 11 / 36.

P(A|B) = (2/36) / (11/36) = 2 / 11.

Therefore, the probability of rolling a sum of 9 with 2 dice, given that at least one die shows 4, is 2/11.

Added 12 days ago|2/23/2026 9:53:32 AM

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