Q. 284.3( 4 Votes )

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

Answer :

**given:** 2 white, 3 red, 5 green, 4 black

**formula:**

two balls are drawn one by one, we have to find the probability that they are of different colours

total possible outcomes are ^{14}C_{2}

therefore n(S)= ^{14}C_{2}=91

let E be the event that all balls are of same colour

E= {WW, RR, GG, BB}

n(E)= ^{2}C_{2}+^{3}C_{2}+^{5}C_{2}+^{4}C_{2}=20

probability of occurrence is

Therefore, the probability of non-occurrence of the event (all balls are different) is

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