Question

Evaluate and provide examples of the differences between using the general addition rule and conditional probability. In what situations are the approaches most applicable? Provide an example of appropriate use of each approach. (300 words)

Answer 1

Let us consider a random experiment, When we throw a die then we get the following sample spaces:

S= {1,2,3,4,5,6}

Let us consider the event of an even number is denoted by A & event f odd number by B.

Then, A= {2,4,6} & B= {1,3,5}

Addition rule: It says that when A & B are two mutually exclusive events then P(A or B)= P(A) + P(B)

Here, A & B are two mutually exclusive events. So,

P(A or B)= P(AUB)= 1= 3/6 + 3/6 = P(A) & P(B)

Conditional Probability: It says that what is the probability of A when an events B has already occurred. i.e. P(A|B)

P(A|B)= P(A∩B)/P(B)

Here let us consider the example, probability of coming an even number in the 2nd trail when it is given that in the 1st trail an odd number has come.

P(A|B)= 3/6 & P(A∩B)/P(B)= ((3/6)*(3/6))/(3/6)= 3/6. Since coming even number in 2nd trail doesn't depend upon then what event coming in the 1st trail. .e. P(A∩B)= P(A)*P(B)