Aspire Faculty ID #17261 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

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:

Solution

Total outcomes when 3 coins tossed:

$2^3=8$

Favourable (all heads or all tails):

HHH, TTT → 2 outcomes

So,

$P(\text{win})=\frac{2}{8}=\frac{1}{4}$

$P(\text{lose})=\frac{6}{8}=\frac{3}{4}$

Expected value:

$E=5\left(\frac{1}{4}\right)+(-3)\left(\frac{3}{4}\right)$

$=\frac{5}{4}-\frac{9}{4}$

$=-\frac{4}{4}$

$=-1$

So expected loss = Rs. 1

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