A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?
A
\(\frac{5}{25}\)
B
\(\frac{7}{20}\)
C
\(\frac{3}{5}\)
D
\(\frac{2}{3}\)
E
\(\frac{5}{6}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Balls were picked without replacement
n( white balls) = 2, n( black balls ) = 3
Total Balls = 2 + 3 = 5 balls
Pr( two balls of different colours ) = WB OR BW
= \(\frac{2}{5} \times \frac{3}{4} + \frac{3}{5} \times \frac{2}{4}\)
= \(\frac{6}{20} + \frac{6}{20}\) = \(\frac{12}{20}\) = \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #26347)