Question

In: Statistics and Probability

Suppose P(A)=.5, P(B)=.4 and P(A and B)=.2 a. Find P(A or B). b. Find P (A...

Suppose P(A)=.5, P(B)=.4 and P(A and B)=.2

a. Find P(A or B).

b. Find P (A and Bc) B complement

c. Find P(A or Bc).

d. Find P(Ac or Bc)

Solutions

Expert Solution

or represents union and 'and' represents intersection

P(A)=.5, P(B)=.4 and =.2

a. Find

Using the addition theorem

= 0.5 + 0.4 - 0.2

b. Find B complement

P(A) can be found out by adding the possible combinations of A with B and B'.

= 0.5 - 0.2

c. Find

P(B') = 1 - P(B) .....Property of complements

=1 - 0.4= 0.6

0.5 + 0.6 - 0.3

d. Find

Again we have the possible combinations of B' with A and A'

= 0.6 - 0.3 = 0.3

P(A') = 1 - P(A)

= 1 - 0.5 = 0.5

0.5 + 0.6 - 0.3

We can also use the identity

= 1 - 0.2

= 0.8

orchestra answered 1 year ago

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