1
$\begingroup$

A bag labeled $A$ contains $4$ red balls and $7$ green balls. Another bag $B$ contains $6$ red and $5$ green balls.

A ball is transferred from bag $A$ to bag $B$, after which a ball is drawn from $B$.

Find the probability that it is a red ball?

To be honest I have no idea how to approach the question, I assume that there would be $12$ balls in the bag $B$ when it has been transferred. I'm lost.

$\endgroup$
  • $\begingroup$ Your assumption is correct. Are you aware of the law of total probability? $\endgroup$ – GFauxPas Aug 14 '15 at 12:46
3
$\begingroup$

Hint:

$$P\left(E\right)=P\left(E\mid R\right)P\left(R\right)+P\left(E\mid G\right)P\left(G\right)$$

Here $R$ is the event that the transferred ball is red, $G$ is the event that the transferred ball is green and $E$ denotes the event that the ball taken out bag $B$ is red.

Second hint: $P\left(E\mid R\right)=\frac7{12}$, why?...

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ I understood what you wrote above to be that, E denotes the event that a ball is taken out of bag A, right ? When the ball is drawn from bag B, is it E + Pr(R) from the second bag ? $\endgroup$ – Mipo Newton Aug 14 '15 at 13:14
  • $\begingroup$ $E$ is (as written) the event that the ball drawn from $B$ is red. If event $R$ has occurred then there are at that moment $7$ red balls in bag $B$ and $12$ in total. That means that $P(E|R)=\frac7{12}$. Here $P(E|R)$ denotes the probability that a red ball is drawn from bag $B$ under the condition that a red ball is transferred from $A$ to $B$. $\endgroup$ – drhab Aug 14 '15 at 13:19
  • $\begingroup$ Yay! I followed it logically and arrived at the teacher's magical answer.35/66 $\endgroup$ – Mipo Newton Aug 14 '15 at 14:02
3
$\begingroup$

Hint:

Think step by step to come back to cases you know.

  1. First step: Transfer a ball

How many different cases are they ? What is the probability of each case ?

  1. Second step: for each case of the previous step: draw a ball

What is the probability to draw each ball ?

  1. Third step: assemble the results of the previous step

You know the results and the probability of every cases. What are the global results ?

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ You should probably label this as a Hint or an Outline $\endgroup$ – Shailesh Aug 14 '15 at 12:57
  • $\begingroup$ Done, thanks for the advice. $\endgroup$ – Amaury Aug 14 '15 at 13:01
  • $\begingroup$ Sorry can you explain further ? $\endgroup$ – Mipo Newton Aug 14 '15 at 13:10
  • $\begingroup$ 1. Transfer a ball from A to B: you either pick a green or red one. You should easily find the probability of each. 2. Let's say you pick a green one. You now know the composition of basket B. You should easily be able to find the probability to pick a green or red ball in basket B. Same process if you pick a red ball from A. 3. You know the probability to pick a green/red ball depending on your first pick. You know the probability to take each ball in A. You should be able to determine the global probability to pick a green/red ball (check drhab's answer). $\endgroup$ – Amaury Aug 14 '15 at 13:28
0
$\begingroup$

You know that ball transferred from A to B is red with 4/11 probability.

Now you have 12 balls in bag B. What is probability it is red? You had 6 red and added 1 with 4/11 probability it is red.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

Hint: there are two cases to consider. One case is that a green ball is moved to bag $B$. The other case is a red ball is moved to bag $B$.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Yes, I got from @drhab, P(E)=P(E∣R)P(R)+P(E∣G)P(G) $\endgroup$ – Mipo Newton Aug 14 '15 at 13:16
  • $\begingroup$ I can visualize it, not just mathematically. $\endgroup$ – Mipo Newton Aug 14 '15 at 13:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.