Q6 of 43 Page 296

In a large metropolitan area, the probabilities are .87, .36, .30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either anyone or both kinds of sets?

Let

E1 = Event that a family owns colour television


E2 = Event that the family owns black and white television


Given that P (E1) = 0.87


P (E2) = 0.36


and P (E1 ⋂ E2) = 0.30


Now, we have to find the probability that a family owns either anyone or both kinds of sets.


By General Addition Rule, we have


P(A ∪ B) = P(A) + P(B) – P(A ∩ B)


∴ P(E1⋃ E2) = P(E1) + P(E2) – P(E1⋂ E2)


= 0.87 + 0.36 – 0.30


= 1.23 – 0.30


= 0.93


Hence, the required probability is 0.93


More from this chapter

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4

An experiment consists of rolling a die until a 2 appears.

(i) How many elements of the sample space correspond to the event that the 2 appears on the kth roll of the die?


(ii) How many elements of the sample space correspond to the event that the 2 appears not later than the kth roll of the die?

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A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.

 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