Q13 of 43 Page 296

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the Probability that

(a) All the three balls are white


(b) All the three balls are red


(c) One ball is red and two balls are white


Given that:


Number of red balls = 8


Number of white balls = 5


∴ Total balls, n = 13


It is given that 3 balls are drawn at random


⇒ r = 3


∴ n(S) = nCr = 13C3


(a) All the three balls are white


We know that,



Total white balls are = 5







(b) All the three balls are red


We know that,



Total red balls are = 8







(c) One ball is red and two balls are white


We know that,









More from this chapter

All 43 →
11

The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P (A ∩ B) = .07. Determine


(a) P (A)


(b)


(c) P (A ∪ B)


(d) P (A ∩ B)


(e) P (B ∩ C)


(f) Probability of exactly one of the three occurs.

 12

One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball.

(a) Write the sample space showing all possible outcomes


(b) What is the probability that two black balls are chosen?


(c) What is the probability that two balls of opposite colour are chosen?

 14

If the letters of the word ASSASSINATION are arranged at random. Find the Probability that

(a) Four S’s come consecutively in the word


(b) Two I’s and two N’s come together


(c) All A’s are not coming together


(d) No two A’s are coming together.

 15

A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.