Question

This question is related to probability, please help ASAP!!!

Bag A contains 3 red balls and 3 blue balls.
Bag B contains 1 red ball and 3 blue balls.
Q: a ball is taken at random from bag A and placed in bag B. Then a ball is chosen from bag B. What is probability that the ball taken from bag B is red... Explain the logic... i know the answer but i dont know the logic behind it please help

Answer 1

What's the probability that the ball you remove is red if you added a red ball from bag A?

Answer 2

2/5

Answer 3

am i right? @Jemurray3

Answer 4

Yes, that's right. What's the probability that the ball you remove is red if you added a blue ball from bag A?

Answer 5

1/5

Answer 6

Lastly, what's the probability that you picked a red marble from bag A? Or a blue one?

Answer 7

1/2

Answer 8

or 3/6

Answer 9

Okay. So the two ways you can end up with a red marble at the end are:
(1) Move a red one from bag A to bag B, and then pick a red one from bag B
(2) Move a blue one from bag A to bag B, and then pick a red one from bag B

Answer 10

yes

Answer 11

The probability of the first one is (1/2) * (2/5) and the probability for the second one is (1/2) * (1/5). Since both sequences give us a red one at the end, you add the probabilities to get the final answer.

Answer 12

yea i know that but the part i didnt understand is why are we multiplying 1/2 with each possibility

Answer 13

Because that's the probability of choosing a red or blue marble from bag A to begin with.

Answer 14

ok its is but why multiplying

Answer 15

@cwrw238 read and just answer my last comment plz

Answer 16

@jim_thompson5910 read and just answer my last comment plz

Answer 17

If you want the probability that you have event A and also event B, you multiply the respective probabilities.

Answer 18

ohh thanx it was very helpful @Jemurray3