Question

a bag contains 3 red 4 Black 2 green balls two balls are drawn at random from the bag find the probability that both balls are of different colours

Answer 1

All the probable results are RR, RB, RG, BB, BG, GG
So the probability of getting balls of different colors is 3/6 = 1/2 = 0.5

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Answer 2

The probability that both balls are of different colors =  0.36

Given:

A bag contains 3 red 4 Black 2 green balls.

Two balls are drawn at random from the bag.

To find:

The probability that both balls are of different colors.

Explanation:

Total number of balls = 9 balls

Out of nine ball 2 ball drawn at random from the bag.

Total number of selection way = $^{9} \mathrm{C}_{2}$

No. of ways to select one red ball = $^{3} \mathrm{C}_{1}$

No. of ways to select one Green ball = $^{2} \mathrm{C}_{1}$

No. of ways to select one Black ball = $^{4} \mathrm{C}_{1}$

No of ways to have a different color ball = RB + RG + BG

                                                            = $^{3} \mathrm{C}_{1}$ × $^{4} \mathrm{C}_{1}$ + $^{3} \mathrm{C}_{1}$ × $^{2} \mathrm{C}_{1}$ + $^{4} \mathrm{C}_{1}$ × $^{2} \mathrm{C}_{1}$

Required probability = $\frac{Total \ number \ of \ selection \ way}{No \ of \ ways \ to \ have \ a \ different \ \ color \ ball}$

Required probability = 0.36

The probability that both balls are of different colors =  0.36

To learn more...

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