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

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(B) When a coin is tossed three times,the sample space $S$ is given by:$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$Total number of outcomes is $8$

Vedclass · Accepted Answer

$1/2$

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(B) When a coin is tossed three times,the sample space $S$ is given by:$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$Total number of outcomes is $8$.Event $E$ is defined as 'head on third toss':$E = \{HHH, HTH, THH, TTH\}$Event $F$ is defined as 'heads on first two tosses':$F = \{HHH, HHT\}$Intersection of $E$ and $F$ is:$E \cap F = \{HHH\}$Probability of $F$ is $P(F) = \frac{n(F)}{n(S)} = \frac{2}{8} = \frac{1}{4}$.Probability of $E \cap F$ is $P(E \cap F) = \frac{n(E \cap F)}{n(S)} = \frac{1}{8}$.Using the formula for conditional probability:$P(E | F) = \frac{P(E \cap F)}{P(F)} = \frac{1/8}{1/4} = \frac{4}{8} = \frac{1}{2}$.

Find $P(E | F)$ for a coin tossed three times,where $E: \text{head on third toss}$,$F: \text{heads on first two tosses}$.

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