A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours
A
\(\frac{36}{625}\)
B
\(\frac{16}{625}\)
C
\(\frac{12}{25}\)
D
\(\frac{13}{25}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Prob(RW or WR) = Prob(RW) + Prob(WR)
\(Prob(R) = \frac{3}{5}:Prob(W) = \frac{2}{5}\\
Prob(RW\hspace{1mm}or\hspace{1mm}WR)=\frac{3}{5}\times\frac{2}{5}+\frac{2}{5}\times \frac{3}{5}\\
\frac{6}{25}+\frac{6}{25}=\frac{12}{25}\)
Source: Myschool Past Questions Archive (Record #26668)