A game consists of tossing a coin 3 times and | vedclass

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(A) The total number of outcomes when tossing a coin $3$ times is $2^3 = 8$. The sample space is $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.The

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$\frac{3}{4}$

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(A) The total number of outcomes when tossing a coin $3$ times is $2^3 = 8$. The sample space is $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.The boy wins if all tosses give the same outcome,which are the events $\{HHH, TTT\}$.The number of winning outcomes is $2$.The number of losing outcomes is $8 - 2 = 6$. These outcomes are $\{HHT, HTH, HTT, THH, THT, TTH\}$.The probability that the boy loses the game is $P(	ext{Lose}) = \frac{	ext{Number of losing outcomes}}{	ext{Total number of outcomes}} = \frac{6}{8} = \frac{3}{4}$.

$A$ game consists of tossing a coin $3$ times and noting its outcome. $A$ boy wins the game if all tosses give the same outcome (i.e.,three heads or three tails) and loses the game otherwise. The probability that the boy loses the game is

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