A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement.
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Answer:
p(x) = probability of x red balls
p(0) = 1/2
p(1) = 1/2
p(2) = 0
Step-by-step explanation:
Total numbers of balls in the bag = 4
1 red and 3 white.
If two balls are drawn one by one without replacement then:
probability of zero red balls = The first ball is not red and the second ball is not red.
=> (³c₂ *²c₁) / ⁴c₁ * ³c₁
=> 6 /12 = 1/2
probability of one red ball = the First ball is red + first is not red and second is red.
=> (¹c₁* ³c₁+ ³c₁ * ¹c₁) / ⁴c₁ * ³c₁
=> 6 / 12 = 1/2
probability of two red ball = First ball is red and second ball is red.
=> (¹c₁*⁰c₁) / ⁴c₁ * ³c₁ = 0
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