Two dice are rolled. Let E = "sum is 8" and F = "at least one die show…

Question

Two dice are rolled. Let E = "sum is 8" and F = "at least one die shows 4". Then P(E|F) equals

Accepted Answer

A. {'text': '1/11', 'label': 'A'}

1. F = {at least one 4}: 11 outcomes among the 36 total two-dice outcomes.
2. E = "sum is 8" = {(2,6),(3,5),(4,4),(5,3),(6,2)}, 5 outcomes.
3. E ∩ F requires sum = 8 AND at least one die = 4: only (4,4). So P(E ∩ F) = 1/36 and P(F) = 11/36.
4. P(E|F) = (1/36) / (11/36) = 1/11.
_Source: NCERT Class 12 Mathematics, Ch 13 "Probability", §13.2_

Answer

{'text': '1/6', 'label': 'B'}

Answer

{'text': '3/11', 'label': 'C'}

Answer

{'text': '5/11', 'label': 'D'}