Three fair coins are tossed. Let E = "at least two heads" and F = "fir…

Question

Three fair coins are tossed. Let E = "at least two heads" and F = "first coin shows tail". Then P(E|F) is

Accepted Answer

A. {'text': '1/4', 'label': 'A'}

1. Sample space of 3 coins has 8 equally likely outcomes.
2. E = {HHH, HHT, HTH, THH}, F = {THH, THT, TTH, TTT}.
3. E ∩ F = {THH}, so P(E ∩ F) = 1/8; P(F) = 4/8 = 1/2.
4. P(E|F) = P(E ∩ F) / P(F) = (1/8) / (1/2) = 1/4.
_Source: NCERT Class 12 Mathematics, Ch 13 "Probability", §13.2_

Answer

{'text': '1/8', 'label': 'B'}

Answer

{'text': '1/2', 'label': 'C'}

Answer

{'text': '3/8', 'label': 'D'}