Question 5Two horses are considered for race. The probability of selec

1.	Question 5Two 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» 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)= 2/51/3=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)=4/52/3+1/31/5 =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

Question 5Two 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»

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

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