Question

A bag P contains 4 white balls and 3 black balls and a bag Q contains 5 white balls and 2 black balls. A ball is drawn at random from P and put into Q. Find the probability that the ball drawn from Q has: 1. The same color as that drawn from P; 2. A different color from that drawn from P;

Answer 1

a)
`P(S)=(15)/(28)`

b)
`P(D)=(13)/(28)`

Explanation:

From the question we are told that:

Bag A
`W=4\\\\ Q=3`

Bag Q
`W'=5\\\\ Q'=2`

Generally the equation for Probability of drawing W&B balls is mathematically given by

Bag A

`P(W)=(4)/(7)P(Q)=(3)/(7)`

Since Ball is drawn and added to Bag Q

Bag Q

`P(W)'=(6)/(8)\\\\ Q(B)'=(2)/(8)`

a)

Generally the equation for Probability of being the same is mathematically given by

`P(S)=(P(W)*P(W'))+(P(B)*P(B)')`

`P(S)=((4)/(7)*(6)/(8))+((3)/(7)*(2)/(8))`

`P(S)=(15)/(28)`

b)

Generally the equation for Probability of NOT being the same is mathematically given by

`P(D)=P(W)+P(B)'+(P(B)*P(W'))`

`P(D)=((4)/(7)*(2)/(8))+((3)/(7)*(6)/(8))`

`P(D)=(13)/(28)`