Question

A throws a coin $4$ times. If he get a head all four times, he is to get a reward of Rs. $240$, on the other hand if he does not get head he is to loose Rs. $24$. He is expected to win

• A. Rs. $50$ Profit
• B. Rs. $10$ Profit
• C. Rs.$25$ Loss
• D. Rs. $7.5$ Loss

Answer 1

Answer: (D)

Rs. $7.5$ Loss

The Sample space for a throw of a coin $4$ times are :

$\Rightarrow S=[HHHH,HHHT,HHTH,HTHH,THHH,TTHH,HHTT,THTH,HTHT,THHT,$

$HTTH,TTTH,TTHT,THTT,HTTT,TTTT]$

$\Rightarrow 2^4=16$

$\Rightarrow$ Probability of getting head on all $4$ throws $=\frac{1}{16}-P_1$

Probability of not getting head on all throws $\frac{15}{16}=p_2$

Expectation $=n_1{p}_1+n_2{p}_2$

$\Rightarrow n_1=Rs.240$ $n_2=Rs.24$

$\therefore 240\times \frac{1}{16}-24\times \frac{15}{16}=15-22.5=Rs.(-7.5)$ Loss.

Hence, the answer is Rs. $(-7.5)$ Loss.