A coin is tossed three times in succession. I | vedclass

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Question

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. Total number of outcomes $n(S) = 8$. Eve

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. Total number of outcomes $n(S) = 8$. Event $E$ is the occurrence of at least two heads: $E = \{HHH, HHT, HTH, THH\}$,so $n(E) = 4$. Event $F$ is the occurrence where the first throw is a head: $F = \{HHH, HHT, HTH, HTT\}$,so $n(F) = 4$. The intersection $E \cap F$ is the set of outcomes where there are at least two heads $AND$ the first throw is a head: $E \cap F = \{HHH, HHT, HTH\}$,so $n(E \cap F) = 3$. The conditional probability is given by: $P\left( \frac{E}{F} \right) = \frac{P(E \cap F)}{P(F)} = \frac{n(E \cap F)}{n(F)} = \frac{3}{4}$.

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P\left( \frac{E}{F} \right) = $

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