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Question
A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability that both are yellow?
Solution
Total number of pencils = 5 + 7 = 12
Let event A : The first pencil chosen is yellow.
∴ P(A) = `(""^7"C"_1)/(""^12"C"_1) = 7/12`
Let event B : The second pencil chosen is yellow.
Since the first yellow pencil is not replaced in the box, we now have 11 pencils, out of which 6 are .
∴ Probability that the second pencil is yellow under the condition that the first yellow pencil is not replaced in the box
= `"P"("B"//"A")`
= `(""^6"C"_1)/(""^11"C"_1)`
= `6/11`
∴ Required probability = P(A ∩ B)
= `"P"("B"//"A")*"P"("A")`
= `6/11 xx 7/12`
= `7/22`.
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