Probability 4 Question 8

8. A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is 13, then the correct option(s) with the possible values of n1 and n2 is/are

(a) n1=4 and n2=6

(b) n1=2 and n2=3

(c) n1=10 and n2=20

(d) n1=3 and n2=6

Passage II

Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appears then 2 balls are drawn at random from U1 and put into U2. Now, 1 ball is drawn at random from U2.

(2011)

Show Answer

Answer:

Correct Answer: 8. (d)

Solution:

P( drawing red ball from B1)=13

n11n1+n21n1n1+n2+n2n1+n2n1n1+n21=13n12+n1n2n1(n1+n2)(n1+n21)=13

Clearly, options (c) and (d) satisfy.

Passage II

Extra close brace or missing open brace

Head appears

Tail appears



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