Q. 7

# Let E_{1} and E_{2} be the events such that and

Find:

(i)P(E_{1}∪ E_{2}), when E_{1} and E_{2} are mutually exclusive.

(ii )P(E_{1}∩ E_{2}), when E_{1} and E_{2} are independent

Answer :

Given: E_{1} and E_{2} are two events such that P(E_{1}) = and P(E_{2}) =

To Find: i)P(E_{1} E_{2}) when E_{1} and E_{2} are mutually exclusive.

We know that,

When two events are mutually exclusive P(E_{1} E_{2}) = 0

Hence, P(E_{1} E_{2}) = P(E_{1}) + P(E_{2})

= +

=

Therefore , P(E_{1} E_{2}) = when E_{1} and E_{2} are mutually exclusive.

ii) P(E_{1} E_{2}) when E_{1} and E_{2} are independent.

We know that when E_{1} and E_{2} are independent ,

P(E_{1} E_{2}) = P(E_{1}) P(E_{2})

=

=

Therefore, P(E_{1} E_{2}) = when E_{1} and E_{2} are independent.

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