If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________

Category: QuestionsIf E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________
Editor">Editor Staff asked 11 months ago

If E and F are two events associated with the same sample space of a random experiment then P (E|F) is given by _________
 
(a) P(E∩F) / P(F), provided P(F) ≠ 0
 
(b) P(E∩F) / P(F), provided P(F) = 0
 
(c) P(E∩F) / P(F)
 
(d) P(E∩F) / P(E)
 
I got this question during an internship interview.
 
This key question is from Conditional Probability in chapter Probability of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (a) P(E∩F) / P(F), provided P(F) ≠ 0
 
To elaborate: E and F are two events associated with the same sample space of a random experiment.
 
The value of P (E|F) = (E∩F) / P(F), provided P(F) ≠ 0. We know that if P(F) = 0, then the value of P(E|F) will reach a value which is not defined hence it is wrong option. Also, P(E∩F) / P(F) and P(E∩F) / P(E) are wrong and do not equate to P(E|F).