# A bag contains 5 red balls, 4 white balls, 2 black balls and 4 green balls. A ball is drawn at random from the big. Find the probability that it is (i) black, (ii) not green, (iii) red or white, (iv) neither red nor green.

Total numbers of elementary events are: 5 + 4 + 2 + 4 = 15

(i) Let E be the event of getting a black ball at the random draw

Then, numbers of favourable outcomes are: 2

P (getting a black ball) = P (E) = 2/15

(ii) Let E be the event of getting non green ball at the random draw

Then, the numbers of unfavourable outcomes are: 4

Probability of getting a green ball = P (green ball) = 4/15

Then, the number of favourable outcome P (not green ball) = 1- P (green ball)

(P non green ball)= P (E) = 1- 4/15 =11/15

(iii) Let E be the event of getting a red or white ball

Let A be the event of getting a red ball

Then, favourable outcomes are: 5

Probability (getting a red ball) = P (A) = 5/15

Let B be the event of getting a white ball

Then, the numbers of favourable outcomes are: 4

Probability (getting white ball) = P (B) = 4/15

P (E) = P (A) + P (B)

P(red ball or white ball) = P (E) = 5/15 + 4/15 = 9/15 = 3/5

(iv) Let E be the event of getting neither red nor green

Let A be the probability of getting a red ball

Then, the favourable outcomes are: 5

P (getting red ball) =P (A) = 5/15

Let B be the event of getting a green ball

Then, the favourable outcomes are: 4

P (getting green ball) = 4/15

Let C be the getting red or green ball

P (getting red or green ball) = P(C) = 5/15 + 4/15 = 9/15 = 3/5

P (getting neither Red nor green ball) = P (E) = 1- P (C) = 1-3/5 = 2/5

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