The probability of event A occurring is P(A)=13/25. The probability of event B occurring is P(B)=9/25. The conditional probability of A occurring given that B has occurred is P(A/B)=5/9.
Determine P(A∪B^') (ie. probability of a union b not), showing your working.
I've tried it, but im getting 26/25, which is wrong.
Determine P(A∪B^') (ie. probability of a union b not), showing your working.
I've tried it, but im getting 26/25, which is wrong.
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......A........... A'
B...........................9/25
B'.........................16/25
....13/25......12/25.....1
P(A/B) = 5/9
P(A/B) = P(A⋂B)/P(B)
P(A⋂B) = P(A/B)*P(B)
P(A⋂B) = (5/9)*(9/25) = 1/5
P(A) = P(A⋂B) + P(A⋂B')
P(A⋂B') = P(A) - P(A⋂B)
P(A⋂B') = 13/25 - 1/5 = 8/25
P(A⋃B') = P(A) + P(B') - P(A⋂B')
P(A⋃B') = 13/25 + 16/25 - 8/25 = 21/25
B...........................9/25
B'.........................16/25
....13/25......12/25.....1
P(A/B) = 5/9
P(A/B) = P(A⋂B)/P(B)
P(A⋂B) = P(A/B)*P(B)
P(A⋂B) = (5/9)*(9/25) = 1/5
P(A) = P(A⋂B) + P(A⋂B')
P(A⋂B') = P(A) - P(A⋂B)
P(A⋂B') = 13/25 - 1/5 = 8/25
P(A⋃B') = P(A) + P(B') - P(A⋂B')
P(A⋃B') = 13/25 + 16/25 - 8/25 = 21/25