Two balls are drawn at random from 1 bag containing 2 white , 3 red , 5 green and 4 black balls one by one without replacement. Find the probability that both balls are different.

Number of white balls (W), red balls (R), black balls (B) and green balls (G) are 2, 3, 4 and 5 respectively.

∴Total numbers of balls in the bag = 2 + 3 + 4 + 5 = 14

Probability that both the balls are of different colour

= 1 – probability that both balls are of same colour.

= 1 – [P(WW) + P (RR) + P(BB) + P(GG)]

= 1 – [P(W) × P(W/W) + P(R) × P(R/R) + P(B) × P(B/B) + P(G) × P(G/G)]

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