Question

If it rains a dealer in raincoats can earn Rs. 500/- a day. If it is fair he will lose Rs. 40/- a day. His mean profit if the probability of a fair day is 0.6 is?
A. Rs. 230/-
B. Rs. 460/-
C. Rs. 176/-
D. Rs. 88/-

Answer 1

Hint: In this question it is given that in rain a dealer in a raincoat can earn Rs. 500/- a day and if it is a fair day then he will lose Rs. 40/- a day. We have found the mean profit if the probability of a fair day is 0.6. So to find the solution we need to know that,
$$P_{1}+P_{2}=1$$………(1)
Where $$P_{1}$$=probability of fair day and $$P_{2}$$=probability of rainy day.
So by using their probability we can find the means profit which is the summation of all the probability multiplied with their profit.

Complete step-by-step solution:
Here given that,
$$P_{1}=0.6$$
Therefore by formula (1) we can write,
$$P_{1}+P_{2}=1$$
$$\Rightarrow P_{2}=1-P_{1}$$
$$\Rightarrow P_{2}=1-0.6=0.4$$
Now also it is given that
Profit on rainy day = Rs. 500 and Loss on fair day = Rs. 40
Let us consider that,
Profit on rainy day = P and Loss on fair day = L
Therefore, P=500 and L=-40(since it is loss so we have to take it as -ve)
$$\text{Mean profit} =P_{2}\cdot P +P_{1}\cdot L$$
                     =$$0.4\times 500+0.6\times \left( -40\right) $$
                     =$$\dfrac{4}{10} \times 500-\dfrac{6}{10} \times 40$$
                     =$$4\times 50-6\times 4$$
                     =$$200-24$$
                     = 176
Therefore the mean profit is Rs. 176/-
Hence the correct option is option C.

Note: While calculating profit or loss in a day you have to remember that if the day is unpredictable i.e, either the day is fair day(you gets profited) or unfair day (you face some loss ) and if you know the probability of a fair or unfair day then mean profit or mean loss is the summation of the multiplication of the probability with its earning.