Two cards are drawn at random from a box which contains 4 card numbered 1,1,2,3. Let X denote the sum of the numbers
on two cards. Find the expected value of
the sum.
Answers
Given : Two cards are drawn at random from a box which contains 4 card numbered 1,1,2,3
X denote the sum of the numbers on two cards
To Find : the expected value of the sum.
Solution:
2 cards are drawn from 4 card
This can be done in ⁴C₂ = 6 ways
( 1 , 1) - Probability = ²C₂/⁴C₂ = 1/6
( 1 , 2) - Probability = ²C₁*¹C₁ / ⁴C₂ = 1/3
( 1 , 3) -Probability = ²C₁*¹C₁ / ⁴C₂ = 1/3
( 2 , 3) Probability = ²C₂/⁴C₂ = 1/6
Sum 1 + 1 = 2 , 1 + 2 = 3 1 + 3 = 4 , 2 + 3 = 5
X P(X) X.P(X)
2 1/6 1/3
3 1/3 1
4 1/3 4/3
5 1/6 5/6
∑X.P(X) 21/6 = 3.5
expected value of the sum. 3.5
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