Question

Question 5 Two horses are considered for race. The probability of selection of first horse is \( \frac{1}{5} \) and that of second is \( \frac{2}{3} \). Find the probability that: (i) both will be selected. (ii) only one of them will be selected. (iii) none of them will be selected. (iv) at least one of them wili be selected.

Answer 1

Let E be the events of selecting first horse .Given that P(E)=1/5 and Let F be the events of selecting 2ND horse .Given that P(F)= 2/3 

THEREFORE P(E^C)=4/5  ,   P(F^C)= 1/3

 (I)BOTH WILL BE SELECTED

P(E and F)= P(EF)=P(E)P(F)= 2/5*1/3=2/15

(ii)  ONLY ONE OF THEM WILL BE SELECTED

P(E^C F)+P(F^CE)= P(E^C)P(F)+P(F^C)P(E)=4/5*2/3+1/3*1/5 =9/15=3/5

(iii) NONE OF THEM WILL BE SELECTED= P(E^CF^C) = P(E^C ) P(F^C) = 4/5 *1/3 = 4/15

(IV)  ATLEAST ONE OF THEM SELECTED= = 1-4/15 = 11/15