urn contains 7 balls of which three are red and four are green. Three balls are chosen randomly from this urn. Let X be the random variable that represents the number of green color balls among the randomly chosen balls. Find Var(X)
Answers
Given : urn contains 7 balls of which three are red and four are green. Three balls are chosen randomly from this urn.
X be the random variable that represents the number of green color balls among the randomly chosen balls.
To Find : Find Var(X)
Solution:
Total = 7
Green = 4
Red = 3
3 can be selected in ⁷C₃ = 35 ways
0 Green can be selected in ⁴C₀.³C₃ = 1 ways
1 Green can be selected in ⁴C₁.³C₂ = 12 ways
2 Green can be selected in ⁴C₂.³C₁ = 18 ways
3 Green can be selected in ⁴C₃.³C₀ = 4 ways
x p px px²
0 1/35 0 0
1 12/35 12/35 12/35
2 18/35 36/35 72/35
3 4/35 12/35 36/35
Total 1 60/35 120/35
12/7 24/7
E(x) = ∑Px = 12/7
Var(X) = ∑px² - (∑Px )²
=> Var(X) = 24/7 - (12/7)²
=> Var(X) = 24/49
Var(X) = 24/49
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