SOLUTION: Let P(A) = P(B) = 1/3 and P(A n B) 1/10, Find the following:
A) P(B')
B) P(A u B')
C) P(B n A')
D) P(A' u B')
Algebra ->
Probability-and-statistics
-> SOLUTION: Let P(A) = P(B) = 1/3 and P(A n B) 1/10, Find the following:
A) P(B')
B) P(A u B')
C) P(B n A')
D) P(A' u B')
Log On
Then,
P(A u B') = P(A) + P(B') - P(A n B') ...... inclusion-exclusion principle
P(A u B') = P(A) + P(B') - [P(A) - P(A n B)] ...... use rule mentioned above
P(A u B') = P(A) + P(B') - P(A) + P(A n B)
P(A u B') = P(B') + P(A n B)
P(A u B') = (2/3) + (1/10)
P(A u B') = (20/30) + (3/30)
P(A u B') = (20+3)/30
P(A u B') = 23/30
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Problem 3
Use a similar trick I did in the previous problem to determine that
P(B n A') = P(B) - P(B n A)
which is the same as
P(B n A') = P(B) - P(A n B)
Furthermore
P(B n A') = P(B) - P(A n B)
P(B n A') = (1/3) - (1/10)
P(B n A') = (10/30) - (3/30)
P(B n A') = (10-3)/30
P(B n A') = 7/30
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Problem 4
P(A' u B') = P( (A n B)' ) ... De Morgans Law
P(A' u B') = 1 - P(A n B) ... complement law
P(A' u B') = 1 - (1/10)
P(A' u B') = (10/10) - (1/10)
P(A' u B') = (10-1)/10
P(A' u B') = 9/10
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