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

.