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(B) In a game,$3$ coins are tossed. The total number of outcomes is $2^3 = 8$.$P(	ext{getting all heads or all tails}) = P(HHH, TTT) = \frac{2}{8} =

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$5$ loss

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(B) In a game,$3$ coins are tossed. The total number of outcomes is $2^3 = 8$.$P(	ext{getting all heads or all tails}) = P(HHH, TTT) = \frac{2}{8} = \frac{1}{4}$.$P(	ext{getting one head or two heads}) = P(HTT, THT, TTH, HHT, HTH, THH) = \frac{6}{8} = \frac{3}{4}$.Let $X$ be the random variable representing the amount won or lost.$P(X = 100) = \frac{1}{4}$.$P(X = -40) = \frac{3}{4}$.The expected value $E(X) = \sum x_i p_i$.$E(X) = 100 	imes \frac{1}{4} + (-40) 	imes \frac{3}{4}$.$E(X) = 25 - 30 = -5$.Since the result is negative,the person expects a loss of ₹ $5$ per game.

$X$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X)$	$0.1$	$0.2$	$0.2$	$0.3$	$0.15$	$0.05$

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$
$P(X = x)$	$K$	$3K$	$5K$	$7K$	$8K$	$K$

In a game,$3$ coins are tossed. $A$ person is paid ₹ $100$,if he gets all heads or all tails; and he is supposed to pay ₹ $40$,if he gets one head or two heads. The amount he can expect to win/lose on an average per game in (₹) is

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