# What is P(A' n B') if P(A)=0.4, P(B)=0.3 and P(A n B)=0.15

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P(A)=0.4

P(B)=0.3

P(A n B)=0.15

Find P(A' n B').

I wanted to confirm if the answer is 0.55 or 0.45, and tell me which method you used to solve this thank you.

P(B)=0.3

P(A n B)=0.15

Find P(A' n B').

I wanted to confirm if the answer is 0.55 or 0.45, and tell me which method you used to solve this thank you.

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#2

(Original post by

P(A)=0.4

P(B)=0.3

P(A n B)=0.15

Find P(A' n B'.

I wanted to confirm if the answer is 0.55 or 0.45, and tell me which method you used to solve this thank you.

**blueynuey**)P(A)=0.4

P(B)=0.3

P(A n B)=0.15

Find P(A' n B'.

I wanted to confirm if the answer is 0.55 or 0.45, and tell me which method you used to solve this thank you.

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#3

answer: P(A' n B';) = 0.45

[finding the probability of just A] P(A n B';) = P(B) - P(A n B) = 0.4 - 0.15 = 0.25

[finding [the probability of just B] P(B n A';) = P(B) - P(A n B) = 0.3 - 0.15 = 0.15

therefore [probability of A or B] P(A u B) = P(A n B';) + P(A n B) + P(B n A';) = 0.25 + 0.15 + 0.15 = 0.55

finally P(A' n B';) = 1 - P(A u B) = 1 - 0.55 = 0.45

[finding the probability of just A] P(A n B';) = P(B) - P(A n B) = 0.4 - 0.15 = 0.25

[finding [the probability of just B] P(B n A';) = P(B) - P(A n B) = 0.3 - 0.15 = 0.15

therefore [probability of A or B] P(A u B) = P(A n B';) + P(A n B) + P(B n A';) = 0.25 + 0.15 + 0.15 = 0.55

finally P(A' n B';) = 1 - P(A u B) = 1 - 0.55 = 0.45

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#4

Assuming your P is a probability space:

P(A n B) = P(A) + P(B) - P(A u B)

Then using De Morgan's Law

P(A' n B') = P(A') + P(B') - P(A' u B')

= P(A') + P(B') - P( (A n B)')

= P(A') + P(B') - ( 1 - P( A n B) )

= ( 1 - P(A) ) ( 1 - P(B) ) - ( 1 - P( A n B) )

P(A n B) = P(A) + P(B) - P(A u B)

Then using De Morgan's Law

P(A' n B') = P(A') + P(B') - P(A' u B')

= P(A') + P(B') - P( (A n B)')

= P(A') + P(B') - ( 1 - P( A n B) )

= ( 1 - P(A) ) ( 1 - P(B) ) - ( 1 - P( A n B) )

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#5

P(A' n B') is the probability that what is not in A intersects with what is not in B. If u draw the venn diagram the answer will become clear.

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#6

**blueynuey**)

P(A)=0.4

P(B)=0.3

P(A n B)=0.15

Find P(A' n B'.

I wanted to confirm if the answer is 0.55 or 0.45, and tell me which method you used to solve this thank you.

P(AuB)= P(A)+P(B)-P(AnB)

and

P(A' n B') = P( (AuB)' ) = 1- P(AuB)

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#7

give formulas correctly...P(A n B' = P(B) - P(A n B)this is a big blunder....in place of P(B) there should beP(A)

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#8

(Original post by

give formulas correctly...P(A n B' = P(B) - P(A n B)this is a big blunder....in place of P(B) there should beP(A)

**vasanti.sai**)give formulas correctly...P(A n B' = P(B) - P(A n B)this is a big blunder....in place of P(B) there should beP(A)

Replying to a post made 3 years ago.... priceless.

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