A bowl contains 10 chips of which 8 are marked Rs.200 each and 2 are marked
Rs.500 each. Let a person draw 3 chips at random from the bowl without
replacement. If the person is to receive the sum of resulting amounts marked on
the drawn chips, find his expectation
Answers
The person's expectation is approximately Rs.264.74.
Given:
A bowl contains 10 chips of which 8 are marked Rs.200 each and 2 are marked Rs.500 each.
Let a person draw 3 chips at random from the bowl without replacement.
To find:
If the person is to receive the sum of resulting amounts marked on the drawn chips, find his expectation
Solution:
To find the person's expectation, calculate the average or expected value of the sums of resulting amounts marked on the drawn chips.
There are two scenarios to consider: when the person draws two chips marked Rs.200 and one chip marked Rs.500, and when the person draws three chips marked Rs.200.
Scenario 1:
Drawing two chips marked Rs.200 and one chip marked Rs.500.
The probability of drawing two chips marked Rs.200
= (8/10) × (7/9) = 56/90.
The probability of drawing one chip marked Rs.500 is (2/8) = 1/4.
The expected value for this scenario
= (200 + 200 + 500) × (56/90) × (1/4) = 900.
Scenario 2: Drawing three chips marked Rs.200.
The probability of drawing three chips marked Rs.200 is (8/10) × (7/9) × (6/8) = 168/180.
The expected value for this scenario
= (200 + 200 + 200) × (168/180) = 186.67.
To find the overall expectation, weigh each scenario by its respective probability:
Overall expectation
= (900 × (56/90) × (1/4)) + (186.67 × (168/180)) =264.74.
Therefore,
The person's expectation is approximately Rs.264.74.
#SPJ1