## Sufiyancs 2 years ago 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

1. Jemurray3

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

2. Sufiyancs

2/5

3. Sufiyancs

am i right? @Jemurray3

4. Jemurray3

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

5. Sufiyancs

1/5

6. Jemurray3

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

7. Sufiyancs

1/2

8. Sufiyancs

or 3/6

9. Jemurray3

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

10. Sufiyancs

yes

11. Jemurray3

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.

12. Sufiyancs

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

13. Jemurray3

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

14. Sufiyancs

ok its is but why multiplying

15. Sufiyancs

16. Sufiyancs

17. Jemurray3

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

18. Sufiyancs

ohh thanx it was very helpful @Jemurray3