Question

In a game. a child will win Rs 5 if he gets all heads or all tails when three coins are tossed simultaneously and he will lose Rs 3 for all other cases. The expected amount to lose in the game is

• A. Rs. 0
• B. Rs. 0.8
• C. Rs. 1
• D. Rs. 2

Answer 1

Answer: (C)

Rs. 1

Answer 2

Assume that $X$ is the amount received by the person.

Thereafter, $X$ can represent values $5$ and $-3$ in a way that

Probability of receiving all heads or all tails when three coins are tossed = $P( X = 5)$

$P( X = 5) = 82​ = 41$ ​

Probability of receiving one or two heads = $P( X = - 3)$

$P(X = -3) = 86 ​= 43$ ​

Hence, per game expected amount is :

=$X= ∑pi​xi​ = 5×41​+(−3)×43 ​=−1$

So, the child , on average, would lose Rs. 1 per toss of the coins.