Q9 of 43 Page 296

Four candidates A, B, C, D have applied for the assignment to coach a school cricket team. If A is twice as likely to be selected as B, and B and C are given about the same chance of being selected, while C is twice as likely to be selected as D, what are the probabilities that

(a) C will be selected?


(b) A will not be selected?

Given that A is twice as likely to be selected as B

i.e. P(A) = 2 P(B) …(i)


and C is twice as likely to be selected as D


i.e. P(C) = 2P(D) …(ii)


Now, B and C are given about the same chance


∴ P(B) = P(C) …(iii)


Since, sum of all probabilities = 1


∴ P(A) + P(B) + P(C) + P(D) = 1


⇒ P(A) + P(B) + P(B) + P(D) = 1 [from (iii)]


[from (i) & (ii)]


[from (iii)]


[from (i)]



⇒ 9P(A) = 4



(a) P(C will be selected) = P(C)


= P(B) [from(iii)]


[from(i)]




(b) P(A will not be selected) = P(A’)


= 1 – P(A)


[By complement Rule]





More from this chapter

All 43 →
7

If A and B are mutually exclusive events, P (A) = 0.35 and P (B) = 0.45, find

(a) P (A′)


(b) P (B′)


(c) P (A ∪ B)


(d) P (A ∩ B)


(e) P (A ∩ B′)


(f) P (A′∩ B′)

 8

A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated

(a) complex or very complex;


(b) neither very complex nor very simple;


(c) routine or complex


(d) routine or simple

 10

One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John’s promotion is same as that of Gurpreet, Rita’s chances of promotion are twice as likely as Johns. Aslam’s chances are four times that of John.

(a) Determine P (John promoted)


P (Rita promoted)


P (Aslam promoted)


P (Gurpreet promoted)


(b) If A = {John promoted or Gurpreet promoted}, find P (A).

 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.