For events A and B it is known that p(A)=p(B) , p(A{intersection} B)=0.1 and p(A{union}B)=0.7 find p(A')?
To find the probability of the complement of event A (A'), you can use the formula:
p(A') = 1 - p(A)
Given that p(A) = p(B) and p(A ∩ B) = 0.1, we need to find p(A ∪ B) to calculate p(A').
We know that p(A ∪ B) = p(A) + p(B) - p(A ∩ B)
Given p(A) = p(B) and p(A ∩ B) = 0.1, we can substitute these values into the equation:
0.7 = p(A) + p(A) - 0.1
0.7 = 2p(A) - 0.1
1 = 2p(A)
p(A) = 1/2
Now, to find p(A'), we substitute the value of p(A) into the formula:
p(A') = 1 - p(A)
p(A') = 1 - 1/2
p(A') = 1/2
Therefore, the probability of event A' is 1/2 or 0.5.