Let
E1,E2 and
A be the events defined as follows:
E1= red ball is transferred from bag
P to bag
QE2= blue ball is transferred from bag
P to bag
QA= the ball drawn from bag
Q is blue
As the bag
P contains 6 red and 4 blue balls,
P(E1)== and P(E2)==Note that
E1 and
E2 are mutually exclusive and exhaustive events.
When
E1 has occurred i.e., a red ball has already been transferred from bag
P to
Q, then bag
Q will contain 6 red and 6 blue balls, So,
P(A∣E1)==When
E2 has occurred i.e., a blue ball has already been transferred from bag
P to
Q, then bag
Q will contain 5 red and 7 blue balls, So,
P(A∣E2)=By using law of total probability, we get
P(A)=P(E1)P(A∣E1)+P(E2)P(A∣E2)=×+×=