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(C) When two coins are tossed,the sample space is $S = \{HH, HT, TH, TT\}$. The total number of outcomes is $4$.Let $X$ be the random variable represe

Vedclass · Accepted Answer

$1/4$

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(C) When two coins are tossed,the sample space is $S = \{HH, HT, TH, TT\}$. The total number of outcomes is $4$.Let $X$ be the random variable representing the prize money.The possible outcomes are:$1$. Two heads $(HH)$: $P(X = 2) = 1/4$. Prize = $Rs. 2$.$2$. One head ($HT$ or $TH$): $P(X = 1) = 2/4 = 1/2$. Prize = $Rs. 1$.$3$. No head $(TT)$: $P(X = -3) = 1/4$. Prize = $-Rs. 3$ (loss).The mean (expected value) $E(X)$ is calculated as:$E(X) = \sum x_i p_i$$E(X) = (2 	imes 1/4) + (1 	imes 1/2) + (-3 	imes 1/4)$$E(X) = 2/4 + 1/2 - 3/4$$E(X) = 1/2 + 1/2 - 3/4 = 1 - 3/4 = 1/4$.Thus,the mean of the prize money is $1/4$.

$A$ player tosses two coins. He wins $Rs. 1$ if $1$ head appears,$Rs. 2$ if $2$ heads appear. But he loses $Rs. 3$ if no head appears. The mean of the prize money is

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