A red ball can be drawn in two mutually exclusive ways. (i) Selecting bag I and then drawing a red ball from it. (ii) Selecting bag II and then drawing a red ball from it Let E1,E2 and A denote the events defined as follows ‌E1=‌ Selecting bag I ‌ ‌E2=‌ Selecting bag II ‌ Since, one of the two bags is selected randomly. ∴P(E1)=‌
1
2
‌ and ‌P(E2)=‌
1
2
Now, P(‌
A
E1
)= Probability of drawing a red ball when the first bag has been selected =4∕7P(‌
A
E2
)= Probability of drawing a red ball when the second bag has been selected =2∕5.