M4maths Previous Puzzles

02 Dec 2014 Probability

There are two bags. First contain 10 white and other 8 red balls. One ball from any bag is shifted to other bag at random. What will be the probability that second ball taken after first event would be red. First event is to drawn first ball.

OPtion

1) 7/13
2) 1/33
3) 33/49
4) 1/49
5) 13/33
6) 1/99
7) 50/101
8) 49/99
9) 47/97
10)None of these

Solution

Initial condition 10W 8R
After first event two possibilities arise
9W
8R;1W
10W, 1R
7R
Choice of any has probability 1/2 so overall probability for getting red ball
= 1/2(1/2*0 + 1/2*8/9) + 1/2(1/2*1/11 + 1/2*1)
solve
49/99
Option 8)

Correct Option: 8 Best Solution (3)