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(A) When $3$ coins are tossed,the total number of outcomes is $2^3 = 8$. The outcomes are: ${HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}$. $P(	ext{all he

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$-0.5$

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(A) When $3$ coins are tossed,the total number of outcomes is $2^3 = 8$. The outcomes are: ${HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}$. $P(	ext{all heads or all tails}) = P({HHH, TTT}) = \frac{2}{8} = \frac{1}{4}$. $P(	ext{one head or two heads}) = P({HTT, THT, TTH, HHT, HTH, THH}) = \frac{6}{8} = \frac{3}{4}$. Let $X$ be the random variable representing the amount won. $P(X = 7) = \frac{1}{4}$ and $P(X = -3) = \frac{3}{4}$. The expected value $E(X) = \sum x_i p_i = 7 	imes \frac{1}{4} + (-3) 	imes \frac{3}{4} = \frac{7}{4} - \frac{9}{4} = -\frac{2}{4} = -0.5$. Thus,the expected amount to win per game is ₹ $-0.5$.

$X=x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X=x)$	$0.1$	$k$	$0.2$	$2k$	$0.3$	$k$

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$K$	$K + \frac{1}{7}$	$2K$	$\frac{2}{5}$

In a game,$3$ coins are tossed. $A$ person is paid ₹ $7$ if he gets all heads or all tails,and he is supposed to pay ₹ $3$ if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

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