Let X be a random variable giving the number of aces in a random draw of 4 cards from an ordinary deck 32 cards. Construct a table showing the probability distribution of X
Answers
Given : X be a random variable giving the number of aces in a random draw of 4 cards from an ordinary deck of 52 cards
To Find : Construct a table showing the probability distribution of X.
Solution:
Total cards = 52
Aces = 4
non aces = 48
4 Cards can be selected in ⁵²C₄ ways
X P(X)
0 ⁴C₀.⁴⁸C₄/⁵²C₄ = ⁴⁸C₄/⁵²C₄ = 0.7187
1 ⁴C₁.⁴⁸C₃/⁵²C₄ = 4.⁴⁸C₃/⁵²C₄ = 0.2556
2 ⁴C₂.⁴⁸C₂/⁵²C₄ = 6.⁴⁸C₂/⁵²C₄ = 0.0245
3 ⁴C₃.⁴⁸C₁/⁵²C₄ = 4.48/⁵²C₄ = 0.0007
4 ⁴C₄.⁴⁸C₀/⁵²C₄ = 1 /⁵²C₄ = 0.000003
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