Multiple choice

A bag contains 3 black and 6 white balls. Two draws of one ball each are made without replacement. What is the probability that one ball is black and the other is white?

  1. 2/9

  2. 1/2

  3. 1/4

  4. 4/9

  5. None of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given situation can be realised in two ways. First  ball is black and then 2nd  ball is white or first  ball is white and 2nd ball is black. So, p(E1) = probabilty of 1st  ball to be black p(E2) = probabilty of 1st ball to be white p(E3) = probabilty of 2nd  ball to be black p(E4) = probabilty of 2nd  ball to be white So, p(E) = p(E1)p(E4) + p(E2)*p(E3)                 = (1/3)(3/4)+(2/3)*(3/8) = 1/2