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Question

There is 30 chance that it rains on any particular day. Given that there is at least one rainy day in a week, what is the probability that there are at least two rainy days in the week?

A
1−4(0.7)71−(0.7)7
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B
4(0.7)71−(0.7)7
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C
1−(0.7)71−4.(0.7)7
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D
(0.7)71−4.(0.7)7
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Solution

The correct option is A 1−4(0.7)71−(0.7)7
Let A be the event that there is at least one rainy day in a week.
Let B be the event that there are at least two rainy days in a week
∴P(BA)=P(A∩B)P(A)=P(B)P(A) as B⊆A
=(1−P(one rainy day or no rainy day))(1−P(no rainiy day))
=1−[7C1(0.3)1(0.7)6+7C0(0.7)7]1−(0.7)7=1−(4)(0.7)71−(0.7)7

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