A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that:

(i) both the balls are white

(ii) one ball is black and the other red

(iii) both the balls are of the same colour

Asked by Aaryan | 1 year ago |  46

##### Solution :-

Given: A bag containing 7 white, 5 black and 4 red balls.

By using the formula,

P (E) = $$\dfrac{favourable\; outcomes }{total\; possible\; outcomes}$$

Two balls are drawn at random, therefore

Total possible outcomes are 16C2

n (S) = 120

(i) Let E be the event of getting both white balls

E = {(W) (W)}

n (E) = 7C= 21

P (E) = $$\dfrac{ n (E) }{ n (S)}$$

=$$\dfrac{21}{120}$$

$$\dfrac{7}{40}$$

(ii) Let E be the event of getting one black and one red ball

E = {(B) (R)}

n (E) = 5C14C= 20

P (E) =$$\dfrac{ n (E) }{ n (S)}$$

$$\dfrac{20}{120}$$

$$\dfrac{1}{6}$$

(iii) Let E be the event of getting both balls of same colour

E = {(B) (B)} or {(W) (W)} or {(R) (R)}

n (E) = 7C2+5C2+4C= 37

P (E) = $$\dfrac{ n (E) }{ n (S)}$$

$$\dfrac{37}{120}$$

Answered by Aaryan | 1 year ago

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