Answer to Question #213703 in Statistics and Probability for Hamza

Question

It is estimated by an insurance company that 90% of total population of age 40--50

years has good health. Using tree diagram finds the probability that: (i) Non (ii) Only

One (iii) Two (iv) All have good health if 3 persons of such age bracket are selected

at random.

Answer 1

Using tree diagram the probability that:

(i) None, (ii) Only One, (iii) Two, (iv) All

have good health if 3 persons of such age bracket are selected are:

(i) None: $C(0; 3)×0.1^3 = 0.001,$

(ii) Only One: $C(1;3)×0.9×0.1^2 = 0.027,$

(iii) Two: $C(2; 3)×0.9^2×0.1 = 0.243,$

(iv) All: $C(3; 3)×0.9^3 = 0.729.$