Q14 of 43 Page 296

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.

Given word is ASSASSINATION

Total number of letters in ASSASSINATION is 13


In word ASSASSINATION, there are 3A’s, 4S’s, 2I’s, 1T’s and 1O’s


Total number of ways these letters can be arranged =


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


If 4S’s come consecutively then word ASSASSINATION become.



So, now numbers of letters is 1 + 9 = 10








(b) Two I’s and two N’s come together



So, now numbers of letters is 1 + 9 = 10








(c) All A’s are not coming together


Firstly, we find the probability that all A’s are coming together


If all A’s are coming together then



So, now numbers of letters is 1 + 10 = 11








Now, P(all A’s does not come together)


= 1 – P(all A’s come together)




(d) No two A’s are coming together


First we arrange the alphabets except A’s




There are 11 vacant places between these alphabets.


Total A’s in the word ASSASSINATION are 3


∴ 3 A’s can be placed in 11 place in 11C3 ways




∴ Total number of words when no two A’s together








More from this chapter

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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?

 13

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

 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.

 16

A sample space consists of 9 elementary outcomes e1, e2, ..., e9 whose probabilities are

P(e1) = P(e2) = .08, P(e3) = P(e4) = P(e5) = .1


P(e6) = P(e7) = .2, P(e8) = P(e9) = .07


Suppose A = {e1, e5, e8}, B = {e2, e5, e8, e9}


(a) Calculate P (A), P (B), and P (A ∩ B)


(b) Using the addition law of probability, calculate P (A ∪ B)


(c) List the composition of the event A ∪ B, and calculate P (A ∪ B) by adding the probabilities of the elementary outcomes.


(d) Calculate P () from P (B), also calculate P () directly from the elementary outcomes of .