Question

In a business venture, a man can make a profit of Rs. $2000$ with probability $0.4$ or have a loss of Rs. $1000$ with a probability $0.6$. His expected profit is:
A) Rs. $800$
B) Rs. $600$
C) Rs. $200$
D) Rs. $400$

Answer 1

Hint: In order to solve this type of problem, At first try to find exact profit and exact loss in the business venture, then subtract the exact loss from the exact profit to find expected profit by the man.

Complete step by step answer:
We have to find expected profit for the man in a business venture.
We are given that In a business venture man makes a profit of Rs.$2000$ with probability of $0.4$
So, the exact profit to the man is given by
$ = $Profit $ \times $ probability given for profit
Substituting the given values in above formula we will get
$
  =>{\text{Exact Profit by the man}} = 2000 \times 0.4 \\
   = 800 \\
 $
And also, he has a loss of Rs. $1000$ with probability of $0.6$
So, the exact loss to the man is given by
$ = $loss$ \times $probability given for loss
$
  =>1000 \times 0.6 \\
   = 600 \\
 $
So, the expected profit will be found when we will subtract the exact loss from the exact profit.
Exact profit $ - $exact loss $ = $Expected profit
Substituting values in above formula we can write
$
 => {\text{Expected profit}} = 800 - 600 \\
   = 200 \\
 $
So, the expected profit of man in a business venture is Rs. $200$
Hence, option C is correct that is Rs 200.


Note:
Expected profit is nothing but the number of amounts when all the profits in business are added and all the loss is subtracted from it. Exact profit and exact loss will be founded when profit and loss will be multiplied with their given probabilities.