Class 12 Maths Probability Multiplication Theorem on Probability

Multiplication Theorem on Probability:

Let E and F be two events associated with a sample space of an experiment.
Then

P(E ∩ F) = P(E) P(F|E), P(E) ≠ 0
= P(F) P(E|F), P(F) ≠ 0

If E, F and G are three events associated with a sample space, then

P(E∩F∩G) = P(E) P(F|E) P(G|E∩F)

Example: In a survey in a class, the probability for a person to watch Examfear videos is 0.8 and the probability for a person to be a topper, if given that he watches Examfear videos is 0.99. find the probability for a person to be both topper and watches Examfear videos.

Solution:
let Event E denotes the event that a person watches Examfear videos
let Event F denotes the event that a person is topper
then P(E) = the probability that a person watches Examfear videos =0.8
and P(F|E)= the probability that a person is a topper if he watches Examfear videos=0.99
then P (E ∩ F)= the probability that a person is both topper and also watches Examfear videos
then according to Multiplication Theorem on probability
P (E ∩ F) = P (E) P (F | E)
= 0.8 x 0.99
= 0.792
∴ The probability that a person is both topper and also watches Examfear
videos = 0.792

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