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Grade 11Algebra

A box contains 12 red and 6 white balls. Balls are drawn from the box one at a time without replacement. If in 6 draws there are at least 4 white balls, find the probability that exactly one white is drawn in the next two draws. (Binomial coefficients can be left as such)

Profile image of Simran Bhatia
12 Years agoGrade 11
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1 Answer

Profile image of Aditi Chauhan
12 Years ago
Hello Student,
Please find the answer to your question
Let us define the following events
A ≡ 4 white balls are drawn in first six draws
B ≡ 5 white balls are drawn in first six draws
C ≡ 6 white balls are drawn in first six draws
E ≡ exactly one white ball is drawn in next two draws (i.e. one white and one red)
Then P (E) = P (E| A) P (A) + P (E| B) P (B) + P (E| C) P (C)
But P (E |C) = 0 [As there are only 6 white balls in the bag.]
P (E) = P (E| A) P (A) + P (E| B) P (B)
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Thanks
Aditi Chauhan
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