probability

[ayushrastogi82]

A bag contains 7 white and 9 black balls. If 2 balls drawn at random, what are the chances of 1 white and 1 black?

[jeromecukier]

there are two possible ways to get a white ball and a black ball,
to get the white ball first then the black ball out of the remaining balls, or to get the black ball first then the white ball out of the remaining balls.

in other terms:

7/16 * 9/15 + 9/16*7/15.

or: 2*7*9/(15*16) = 21/40


another way to look at this problem is to count the chances of having 2 white or 2 black balls.
white balls: (7*6)/(16*15); black balls: (9*8)/(16*15), so (42+72)/(240) = 114/240 or 19/40. chance to have one of each colour is 1 minus that or 21/40.

[Ben Ku]

ayushrastogi82, it would be helpful to, in addition to the problem, describe what you did, where you got stuck, or what you didn't understand.

jeromecukier's solution is good. Let me know if you have further questions.