Find P(E | F) for a coin tossed three times,w | vedclass

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Question

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$.The event $E$ (at least two heads) is: $E

Vedclass · Accepted Answer

$\frac{3}{7}$

Vedclass · Answer

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$.The event $E$ (at least two heads) is: $E = \{HHH, HHT, HTH, THH\}$.The event $F$ (at most two heads) is: $F = \{HHT, HTH, HTT, THH, THT, TTH, TTT\}$.The intersection $E \cap F$ is: $E \cap F = \{HHT, HTH, THH\}$.Calculating the probabilities:$P(E \cap F) = \frac{n(E \cap F)}{n(S)} = \frac{3}{8}$.$P(F) = \frac{n(F)}{n(S)} = \frac{7}{8}$.Using the formula for conditional probability:$P(E | F) = \frac{P(E \cap F)}{P(F)} = \frac{\frac{3}{8}}{\frac{7}{8}} = \frac{3}{7}$.

Find $P(E | F)$ for a coin tossed three times,where $E$ is the event 'at least two heads' and $F$ is the event 'at most two heads'.

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