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 A bag contains 5 balls out of which some or maybe all are black. 2 balls are drawn from the bag and both are found to be black. What is the probability that all balls in the bag are black?
  • a)
    0.5
  • b)
    0.7
  • c)
    0.8
  • d)
    0.9
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A bag contains 5 balls out of which some or maybe all are black. 2 bal...
Since 2 black balls were drawn, the number of black balls may be either of 2,3,4,5.
Let A2 = bag contains 2 black balls
A3 = bag contains 3 black balls
A4 = bag contains 4 black balls
A5 = bag contains 5 black balls
E = 2 black balls are drawn
P(E / A2) = 2C2 / 5C2 = 1/10
P(E / A3) = 3C2 / 5C2 = 3/10
P(E / A4) = 4C2 / 5C2 = 3/5
P(E / A5) = 5C2 / 5C2 = 1
Since the number of black balls is unknown, all events A2, A3, A4, A5 are equally likely.
So, P(A2) = P(A3) = P(A4) = P(A5) = 1/4
By Bayes’ theorem,
P(A5 / E) = {P(A5) X P(E / A5) } / [{P(A2) X P(E / A2) } + {P(A3) X P(E / A3) } + {P(A4) X P(E / A4) } + {P(A5) X P(E / A5) }]
P(A5 / E) = {1/4 X 1} / [{1/4 X 1/10} + {1/4 X 3/10} + {1/4 X 3/5} + {1/4 X 1}]
P(A5 / E) = 1/2 = 0.5
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A bag contains 5 balls out of which some or maybe all are black. 2 balls are drawn from the bag and both are found to be black. What is the probability that all balls in the bag are black?a)0.5b)0.7c)0.8d)0.9Correct answer is option 'A'. Can you explain this answer?
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