Q57 / 150 · MHT CET 2024 (10 May Shift 1) · Mathematics

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

  • A
    10 loss
  • Correct answer
    B
    5 loss
  • C
    5 gain
  • D
    10 gain

Solution

In a game, 3 coins are tossed. $\mathrm{P}($ getting all heads or all tails $)=\frac{2}{8}=\frac{1}{4}$ $\mathrm{P}($ getting one head or two heads $)=\frac{6}{8}=\frac{3}{4}$ Let $x$ : number of rupees the person gets. $\begin{aligned} & P(X=100)=\frac{1}{4} \\ & P(X=-40)=\frac{3}{4} \end{aligned}$ $\therefore \quad$ The amount he can expect to win $=$ mean $\begin{aligned} & =\sum \mathrm{n}_{\mathrm{i}} \mathrm{p}_{\mathrm{i}} \\ & =100 \times \frac{1}{4}+(-40) \times \frac{3}{4} \\ & =\frac{100}{4}-\frac{120}{4} \\ & =-5 \\ & =5 \mathrm{loss} \end{aligned}$

Hence, the correct answer is option: 'B'.

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