Probability 3 Question 23

23. Let E and F be two independent events. The probability that exactly one of them occurs is 1125 and the probability of none of them occurring is 225. If P(T) denotes the probability of occurrence of the event T, then

(2011)

(a) P(E)=45,P(F)=35

(b) P(E)=15,P(F)=25

(c) P(E)=25,P(F)=15

(d) P(E)=35,P(F)=45

Show Answer

Solution:

P(EF)P(EF)=1125

[i.e. only E or only F ]

Neither of them occurs =225

P(E¯F¯)=225

From Eq. (i), P(E)+P(F)2P(EF)=1125

From Eq. (ii),

(1P(E))(1P(F))=225

1P(E)P(F)+P(E)P(F)=225

From Eqs. (iii) and (iv),

P(E)+P(F)=75 and P(E)P(F)=1225P(E)75P(E)=1225(P(E))275P(E)+1225=0P(E)35P(E)45=0P(E)=35 or 45P(F)=45 or 35



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक