Question

Bag A contains 5 white and 4 black balls, and bag B contains 7 white and 6 black balls. One ball is drawn from bag A and without noticing its colour, is put in the bag B. If a ball is then drawn from bag B, find the probability that it is black in colour.

Answer 1

Answer:

$\frac{29}{63}$ is the probability that it is black in colour

Step-by-step explanation:

Explanation:

Given , Bag A contain 5 white balls and 4 black balls.

In bag B contains 7 white balls and 6 black balls

Let X be the event that black ball is drawn from bag B .

Step1:

Let $E_{1}$ be the event that white ball is drawn from bag A

   $P(E_{1} )$ = $\frac{5}{9}$

Now , probability that the black ball is drawn from bag B

$P(\frac{X}{E_{1} }) = \frac{6}{14}$

let $E_{2}$ be the event that black ball is drawn from bag A

$p(E_{2} ) = \frac{4}{9}$

So , the probability that  the black ball is drawn from the bag B

$p(\frac{X }{E_{2}} ) = \frac{7}{14}$

Step2:

There fore the probability that black ball is drawn from bag B

= $P(E_{1} ).P(\frac{X}{E_{1} }) + p(E_{2} ) .p(\frac{X }{E_{2}} )$

=$\frac{5}{9}. \frac{6}{14} + \frac{4}{9}.\frac{7}{14}$

= $\frac{30}{126} +\frac{28}{126} = \frac{58}{126}$

= $\frac{29}{63}$

Final answer :

Hence ,  the probability that it is black  colour  is $\frac{29}{63}$.

Answer 2

Answer:

The probability that it is black in colour is $\frac{29}{63}$.

Step-by-step explanation:

As per the data given in the question,

We have,

Bag A contains 5 white and 4 black balls

Bag B contains 7 white and 6 black balls

Case(i)

probability of taking out white ball from Bag A = $\frac{5}{9}$

Then, taking black from Bag B after the given action = $\frac{6}{14}$

Overall probability = $\frac{5}{9} \times \frac{6}{14} = \frac{30}{126}$

Case(ii)

probability of taking out black ball from Bag A = $\frac{4}{9}$

Then, taking black from Bag B after the given action = $\frac{7}{14}$

Overall probability = $\frac{4}{9} \times \frac{7}{14} = \frac{28}{126}$

So, overall probability

$\frac{30}{126} +\frac{28}{126} = \frac{58}{126} =\frac{29}{63}$

Hence, the probability that it is black in colour is $\frac{29}{63}$

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