What is the number of sample points in a simple event associated with an experiment?

Gold number is associated with

True or false If E be an event associated with an experiment then P(E')=1-P(E).

True or false If A and B are independent events associated with an experiment, then P(AcapB)=P(A)+P(B) .

A,B and C are three mutually exclusive and exhaustive events associated with a random experiment . Find P(A) given that P(B)=(3)/(2)P(A)andP(C )=(1)/(2)P(B) .

If A,B,C are mutually exclusive and exhausive events associated with an experiment, then P(A)+P(B)+P( C)=1.

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment : A : the sum is even B : the sum is a multiple of 3 C : the sum is less than 4 D : the sum is greater than 11. Which of these events are mutually exclusive ?

If the probability distribution of a random variable X associated with an experiment is find the vlalue of k.

Prove that P(A)= P(AcupB)+P(AcapB) , where A and B are any two events associated with an experiment.

Prove that P(AcupB)=P(AcapB)+P(AcapbarB)+P(barAcapB) , where A and B are any two events associated with an experiment.

True or false If A and B are two events associated with an experiment such that P(A)>0 and also P(B)>0, then A and B can be both mutaully exclusive and independent.