A bag contains 7 red and 4 black identical balls. Two balls were picked at random from the bag and replaced each time. Find the probability the two balls were of same colour.
A
\(\frac{54}{121}\)
B
\(\frac{65}{121}\)
C
\(\frac{29}{55}\)
D
\(\frac{27}{55}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Total Balls 7 + 4 = 11
Probability of Picking Two Balls of the Same Colour = RR or BB = \(\frac{7}{11} \times \frac{7}{11}\) + \(\frac{4}{11} \times \frac{4}{11}\)
= \(\frac{49}{121}\) + \(\frac{16}{121}\) = \(\frac{65}{121}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70292)