# A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

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A bag contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) White

(ii) Red

(iii) Not black

(iv) Red or white

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Total no. of possible outcomes = 15 {4 red, 5 black, 6 white balls}

(i) E ⟶ event of drawing white ball.

No. of favourable outcomes = 6 {6 white}

Probability, P(E) = (No. of favorable outcomes)/(Total no.of possible outcomes)

P(E) = 6/15 = 2/5

(ii) E ⟶ event of drawing red ball

No. of favourable outcomes = 4 {4 red balls}

P(E) = 4/15

(iii) E ⟶ event of drawing black ball

No. of favourable outcomes = 5 {5 black balls}

P(E) = 5/15 = 1/3

Bar E⟶ event of not drawing black ball

P(Bar E) = 1 − 1/3  = 2/3

(iv) E ⟶ event of drawing red or white ball

No. of favourable outcomes = 10 {4 red & 6 white}

P(E) = 10/15 = 2/3