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(a) a box contains 4 red balls, 3 white balls, and 3 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)

Answer :

The probability of getting a red ball on the first draw and a white ball on the second is 0.3.

Total number of balls = 10

Now we have to pick: 4 red balls or 3 black balls or 3 white balls.

Case-1:

In this case we pick 4 red balls.

Now, probability for picking one red ball is 3/10.  Now, the 2nd ball is drawn which is also red, probability for picking 2nd red ball is 2/19. probability for picking two red balls is

P(r) = (3/10) (2/9)

Case-2:

In this case we pick 3 white balls

Probability for picking 3 white balls

P(w) = (3/10) × (4/9)

Case-3:

probability for picking 03 black balls:

P(b) = (03/10) (02/9)

Therefore, probability for picking 2 same color balls:

= (3/10) (2/9) +(03/10) × (04/9) +(03/10) (02/9)

= 0.3

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