A bag contains 4 white ball 5 black balls are drawn at random what is the probability of both are the same colours.?

Question

Answer

Probability of Drawing Same Coloured Balls

Given Information

4 white balls

5 black balls

Calculation of Probability

There are two possibilities when drawing two balls:

Both balls are white

Both balls are black

The probability of drawing two white balls:

P(white ball) = 4/9

P(second white ball) = 3/8 (since there is one less white ball in the bag)

P(both white balls) = (4/9) x (3/8) = 12/72

The probability of drawing two black balls:

P(black ball) = 5/9

P(second black ball) = 4/8 (since there is one less black ball in the bag)

P(both black balls) = (5/9) x (4/8) = 20/72

Total Probability of Same Coloured Balls

The probability of drawing same coloured balls is the sum of the probability of drawing two white balls and the probability of drawing two black balls:

P(same coloured balls) = 12/72 + 20/72 = 32/72 = 4/9

Explanation

The probability of drawing same coloured balls is 4/9. This means that the chances of drawing both white balls or both black balls is 4 out of 9. In other words, if the experiment of drawing two balls is repeated many times, in the long run, we can expect that the same coloured balls will be drawn 4/9 of the time.

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