There are two boxes 1 and 2. Box 1 contains 3 red and 6 black balls.box 2 contains 5 red and n black balls.one of the two boxes is drawn at random.the ball drawn is found to be red.if the probability that this red ball comes out from box 2 is 3/5,find the value of n.
Answers
Answer:
Another Bayes' theorem question
I think this is the answer
at least that's what I did in my board exam.
Tell me if I'm wrong I'll be happy to improve
Answer:
n = 5
Step-by-step explanation:
There are two boxes 1 and 2. Box 1 contains 3 red and 6 black balls.box 2 contains 5 red and n black balls.one of the two boxes is drawn at random.the ball drawn is found to be red.if the probability that this red ball comes out from box 2 is 3/5,find the value of n.
Box 1 - 3 Red , 6 Black
Probability of red from Box 1 = 3/(3+6) = 3/9 = 1/3
Probability of Black from Box 1 = 6/(3+6) = 6/9 = 2/3
Box 2 - 5 Red , n Black
Probability of red from Box 2 = 5/(5+n)
Probability of Black from Box 2 = n/(5+n)
Probability of red from Box 2 / (Probability of red from Box1 + Box 2) = 3/5
=> n/(5+n) / ( n/(5+n) + 1/3 ) = 3/5
=> 5n/ (5+n) = 3n/(5+n) + 1
=> 2n/(5+n) = 1
=> 2n = 5 + n
=> n = 5
5 Black Balls