[pop000]

in the first question I have dilemma between option C to option D .

in the second question A and B are events I need to decide what value x can get.
so here I think is answer B.

do I correct?

thanks.

[jcaron2]

Pop, I'm guessing you scanned or attached a picture of the questions, but for some reason they're not showing. I tried it in both skins, and I can't see anything.

[pop000]

Oh yes you are correct I forgot to put the picture :) sorry.
Here the picture:

[jcaron2]

Pop, are you familiar with De Morgan's Laws?



Also, keep in mind that



Hence, the answer to the first question is D.


As for the second question, if you're trying to find the intersection of two events, the probability of both happening is clearly less than or equal to the probability of either one of them individually. Hence, you know x <= 0.5. Likewise, if you envision the total event space as a square of area 1.0, one event occupies 50% of that space, and the other occupies 70% of it. You can't possibly fit both events into the square without some overlap. For example, if you picture event A occupying the left 50% of the square, and event B occupying the right 70% of the square, there is an overlap of 20%. There's no way to squeeze the two events into the box with less overlap than that. Hence, you also know x >= 0.2. There's only one answer that meets the criterion that 0.2 <= x <= 0.5, and you got it right. Good job!

[pop000]

Thanks you for your answer :)
And yes I know the De Morgan's Law.;)