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(B) When $3$ coins are tossed,the total number of outcomes is $2^3 = 8$. The sample space is $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$.$1$. Cas

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(B) When $3$ coins are tossed,the total number of outcomes is $2^3 = 8$. The sample space is $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$.$1$. Case $1$: Getting all heads or all tails.The outcomes are $HHH$ and $TTT$. There are $2$ such outcomes.The probability $P(	ext{win } ₹150) = \frac{2}{8} = \frac{1}{4}$.$2$. Case $2$: Getting one head or two heads.The outcomes are $HHT, HTH, THH, HTT, THT, TTH$. There are $6$ such outcomes.The probability $P(	ext{lose } ₹50) = \frac{6}{8} = \frac{3}{4}$.$3$. Expected value $E(X)$:$E(X) = (150 	imes \frac{1}{4}) + (-50 	imes \frac{3}{4})$$E(X) = \frac{150}{4} - \frac{150}{4} = 0$.Therefore,the expected amount he can win or lose on an average per game is $₹0$.

$X$	$1$	$2$	$3$	$4$	$5$	$6$
$F(X=x)$	$0.2$	$0.37$	$0.48$	$0.62$	$0.85$	$1$

In a game,$3$ coins are tossed. $A$ person is paid $₹150$ if he gets all heads or all tails,and he is supposed to pay $₹50$ if he gets one head or two heads. The amount he can expect to win or lose on an average per game in $₹$ is:

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