### Problem 6 - black or blue

Hope that the small things you are learning here are increasing your knowledge arrows in your quiver. CAT is near. Happy hunting.

You have a ball in a bag. It is either a yellow tennis ball or a red cricket ball with equal likelihood. We dont know which one is inside.

Roger comes in and adds a yellow tennis ball into the bag.

Rafael comes and pulls out a ball from the bag. The ball he pulls out is a tennis ball.

What is the probability that the other ball remaining in the bag is a tennis ball.

The answers are 1) 1/3 2) 2/3 3) 1/4 4) 3/4

Hint: The probability was .5 before Roger added the ball. Since the four answers above are spread on both side of .5, first think if the probability shud increase or decrease.

Click here for the answer

**Now the question**You have a ball in a bag. It is either a yellow tennis ball or a red cricket ball with equal likelihood. We dont know which one is inside.

Roger comes in and adds a yellow tennis ball into the bag.

Rafael comes and pulls out a ball from the bag. The ball he pulls out is a tennis ball.

What is the probability that the other ball remaining in the bag is a tennis ball.

The answers are 1) 1/3 2) 2/3 3) 1/4 4) 3/4

Hint: The probability was .5 before Roger added the ball. Since the four answers above are spread on both side of .5, first think if the probability shud increase or decrease.

Click here for the answer

## 3 Comments:

cant think of any exact procedure to get the answer..but tempted to make a choice as 3/4.

Here is a post by Praful who had sent it to catfundae@gmail.com as he could not comments are blocked at office - Gyan-ee

my go at prob 6:

2 cases r probable: rafael either pulled out the yellow ball roger added or he took out the earlier one-- each has equal prob of 0.5

so the probability that the ball left out is yellow is : 0.5(prob of taking the original ball out) + 0.5*0.5 (prob of taking roger's ball out * prob of original ball which is left being yellow is 0.5)

=.5+.25 =3/4.

P.S. i am replying by mail since comments are blocked in my office by a firewall.

Praful.

The answer is 2/3.

To think simple, let us list out the equally likely scenarios.

1. First ball was tennis. Second ball was tennis. Rafael pulled first ball

2. First ball was tennis. Second ball was tennis. Rafael pulled second ball

3. First ball was cricket. Second ball was tennis. Rafael pulled second ball

Out of the three cases, two correspond to the first ball being tennis. Hence the answer is 2/3

Note: If we had not known that Rafael had pulled out Tennis ball, then there would be one more scenario - First ball was tennis. Second ball was tennis. Rafael pulled first ball

People go wrong when you take the conditional probability approach and fall into the 3/4 trap.

You analyse the problem as "With two equally likely scenarios, what is the probability of getting a tennis ball". The answer for that question in 3/4. In this question, that event has already happened and the question is the probability of the another ball being the tennis ball.

Think deep and understand the difference I have stated above very carefully so that you dont get hunted by CAT.

Praful, your mistake is in the assumption that the probability of rafael pulling yellow ball in each case is 0.5. Those cases are mutually exclusive and exhaustive, but not equally likely.

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