A player tosses two coins. He wins Rs.1 if 1 head appears, Rs.2 if 2 heads appear. But he lose Rs 5 if no head appears. The mean of the prized money is

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$\frac{1}{2}$

$\frac{1}{4}$

- $\frac{1}{4}$

$\frac{1}{5}$

answer is C.

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Detailed Solution

$P (X = 0) = \frac{^{2} C_{0}}{2^{2}} = \frac{1}{4}, P (X = 1) = \frac{^{2} C_{1}}{2^{2}} = \frac{2}{4} = \frac{1}{2}, P (X = 2) = \frac{^{2} C_{2}}{2^{2}} = \frac{1}{4}$

Number of heads	0	1	2
profit/loss	-5	1	2
P(X=x)	1/4	1/2	1/4

$Mean = μ = \sum x_{r} . P (x = x_{r}) ∴ Mean = (- 5) \frac{1}{4} + (1) \frac{1}{2} + (2) \frac{1}{4} = - \frac{1}{4}$

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