Probability 3 Question 26

26. Let E and F be two independent events. If the probability that both E and F happen is 1/12 and the probability that neither E nor F happen is 1/2. Then,

(a) P(E)=1/3,P(F)=1/4

(1993,2M)

(b) P(E)=1/2,P(F)=1/6

(c) P(E)=1/6,P(F)=1/2

(d) P(E)=1/4,P(F)=1/3

Show Answer

Solution:

  1. Both E and F happen P(EF)=112 and neither E nor F happens P(E¯F¯)=12

But for independent events, we have

P(EF)=P(E)P(F)=112

and

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

12=1P(E)+P(F)+112P(E)+P(F)=112+112=712

On solving Eqs. (i) and (ii), we get

 either P(E)=13 and P(F)=14 or P(E)=14 and P(F)=13



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक