Question

Give P (A ) = 0.60 P ( b) = 0.40 P ( A B ) = 0.24 . find p ( A / B ) P ( B / A ) and P ( A B ) . what is the relation ship between A and B

Answer 1

Answer:

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Answer 2

The values of P(A/B), P(B/A), and P(A∪B) are 0.6, 0.4, and 0.76 respectively.

Given:

P(A)= 0.60

P(B)= 0.40

P(A∩B)= 0.24

To Find:

The values of P(A/B), P(B/A), and P(A∪B)

Solution:

• P∪Q stands for the union of the two sets P and Q.
• This is the collection of all the various components that make up P or Q.
• The symbol  ∪ denotes the union of a set.
• P∩Q is a symbol for the intersection of the sets P and Q.
• This is the collection of every element that both P and Q contain.
• The symbol ∩ denotes the intersection of a set.

We know that,

P(A/B)= P(A∩B) / P(B)

           =0.24/0.40 = 0.6

P(B/A)= P(A∩B) / P(A)

          = 0.24/0.60 = 0.4

Now,

P(A∪B)= P(A)+ P(B)- P(A∩B)

           = 0.60+0.40-0.24= 0.76

Hence, the values of P(A/B), P(B/A), and P(A∪B) are 0.6, 0.4, and 0.76 respectively. A and B here represent two separate events whose probability is represented by P(A) and P(B) respectively.

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