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.
Total Balls 7 + 4 = 11
Probability of Picking Two Balls of the Same Colour = RR or BB = \(\frac{7}{11} \times \frac{7}{11}\) + \(\frac{4}{11} \times \frac{4}{11}\)
= \(\frac{49}{121}\) + \(\frac{16}{121}\) = \(\frac{65}{121}\)
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