UPSC NDA II 2015 Mathematics Solved Paper

P (one white ball & one black ball )
P {[black from 1 st bag & white from 2nd] or [white from 1 st & black from 2nd]}
=P([B1∩W2)∪(W1∩B2)]
=P(B1∩W2)+P(W1∩B2)
(By addition theorem for mutually exclusive events)
=P(B1)P(W2)+P(W1)P(B2)
(∴B2 & W2;B2 & W1are pairs of independent events)
=[‌‌

2

6

×‌‌

3

8

]+[‌‌

4

6

×‌‌

5

8

]
=

13

24