A bag contains 3 red, 4 black and 5 green identical balls. Two balls are picked at random, one after the other without replacement. Find the probability that one is red and the other is green
A
\(\frac{2}{3}\)
B
\(\frac{5}{11}\)
C
\(\frac{5}{22}\)
D
\(\frac{5}{24}\)
E
\(\frac{5}{48}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Total balls = 12
RG or GR
\(\frac{3}{12}\) x \(\frac{5}{11}\) + \(\frac{5}{12}\) x \(\frac{3}{11}\)
= \(\frac{5}{44}\) + \(\frac{5}{44}\)
=\(\frac{10}{44}\)
=\(\frac{5}{22}\)
Source: Myschool Past Questions Archive (Record #23838)