Actex problem set2-7

[alenblue]

Dear All

In this question I cant figure out why choices d and e are false .
In the answer it just mention b is ture .
I have no idea to determine formulas although I have check some of text books .
Whould someone can help me ?Thanks .

Have a nice weekend

[RossMoney2120]

Utilize the complements. You should know that A u B|C = A|C + B|C - A n B|C. Therefore, A' u B'|C = A'|C + B'|C - A' n B'|C. Plug in the information given and see which statements are true. Hope this helps!

[alenblue]

Thanks for repling
I know this complement and get the answer is b .
I am courious what concepts being lose that I cant get why the d and e are false .
Someone tell me I should apply P(a union b l c)+P(a union b l c")=P(a union b) and this formula can explain why d is false .
Because I never see the formula at text books I examine it by venn diagram it seem to be have problems .

[Ultra_Dank]

what are the numbers in the problem? Numbers are to blurry when I try to enlarge.

[daaaave]

I can't read the OP that well, but it looks like it is an old exam 110 problem from 1990, which says (I apologize for formatting problems, I'm copying and pasting from a PDF):

Let A, B, and C be events such that P[A | C] = 0.05 and P[B | C] = 0.05. Which of the following statements must be true?
A. P[AB | C] = 0.05^2 B. P[A′B′ | C] ≥ 0.90 C. P[A ∪ B | C] ≤ 0.05 D. P[A′ ∪ B′ | C] ≥ 1 − (0.05)^2 E. P[A ∪ B | C] ≥ 0.10

There are two points in the problem. One is that the probabilities conditioned on C are still probabilities, so our usual rules of probability still hold. Then given that, the inequalities in C and E are reversed, making those false, and the statements for A and D require writing P[AB] as P[A]*P[b] or P[A' B'] as P[A']*P[B'], both of which require independence which need not hold making those statements false as well.

[alenblue]

Thanks for repling
The OP have some different in choices D and E
The D. P[A ∪ B | C^'] ≥ 1 − (0.05)^2 E. P[A ∪ B | C^'] ≥ 0.10
How can I get the P( A l C' ) and P( B l C' ) ?