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

1. 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.
2. (Original post by 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.
try drawing a Venn diagram of A and B, their intersection will be 0.15, you want to find the probability outside of both circles
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
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) )
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.
6. (Original post by 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.
I'd use:

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

and

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

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