Probability 4 Question 7

7. One of the two boxes, box I and box II was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II, is 13, then the correct option(s) with the possible values of n1,n2,n3 and n4 is/are

(a) n1=3,n2=3,n3=5,n4=15

(b) n1=3,n2=6,n3=10,n4=50

(c) n1=8,n2=6,n3=5,n4=20

(d) n1=6,n2=12,n3=5,n4=20

Show Answer

Answer:

Correct Answer: 7. (b)

Solution:

n1 Red n2 Black |n3 Red n4 Black |Box I 

Let A= Drawing red ball

P(A)=P(B1)P(A/B1)+P(B2)P(A/B2)

=12n1n1+n2+12n3n3+n4

Given, P(B2/A)=13

P(B2)P(B2A)P(A)=1312n3n3+n412n1n1+n2+12n3n3+n4=13n3(n1+n2)n1(n3+n4)+n3(n1+n2)=13

Now, check options, then clearly options (a) and (b) satisfy.



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