There are two boxes I and II . Box I contains 3 red and 6 black balls .Box II contains 5 red and 'n' black balls. One of the two boxes, box I and box II is selected at random and a ball is drawn at random. The ball drawn is found to be red. If the probability that this red all comes out from box II is 3/5, find the value of 'n'.
Answers
Answer:
Step-by-step explanation:
Box 1 - Red Ball Probability = 3/9 = 1/3
Box 1 - Black Ball Probability = 6/9 = 2/3
Box 2 - Red Ball Probability = 5/(5+n)
Box 2 - Black Ball Probability = n/(5+n)
Probability that red all comes out from box II is 3/5 when box is selected at random.
Probability of red from Box 2 / (Probability of red from Box1 + Probability of red from Box 2) = 3/5
∴ n/(5+n) / ( n/(5+n) + 1/3 ) = 3/5
∴ 2n = 5 + n
∴ n = 5
Hence there are 5 Black Balls.
Answer:
5 Black Balls
Step-by-step explanation:
There are two boxes I and II . Box I contains 3 red and 6 black balls .Box II contains 5 red and 'n' black balls. One of the two boxes, box I and box II is selected at random and a ball is drawn at random. The ball drawn is found to be red. If the probability that this red all comes out from box II 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