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Question : 38 of 160
Marks:
+1,
-0
Solution:
We have,
P(E1)=‌ and
P(E1∪E2)=‌.
Since,
E1 and
E2 are independent events
∴‌‌P(E1∩E2)=P(E1)×P(E2) Let
P(E2) be
x.
Then,
‌‌P(E1∩E2)=‌ ∵‌‌P(E1∪E2)=P(E1)+P(E2)−P(E1∩E2)
⇒‌‌‌=‌+x−‌ ⇒‌‌‌=‌+‌ ⇒‌‌‌=‌−‌=‌=‌ ⇒‌‌‌‌‌=‌⇒x=‌ ∴‌‌P(E2)=‌ and
‌‌P(E1∩E2)=‌=‌ Now,
=‌=‌=‌×2=‌
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