2011 VCAA Paper 2 MCQ 21

[destain]

Staring at the solutions but have no clue as to what they're saying

[BubbleWrapMan]

If P and Q are independent then so are P' and Q

So , and

If , then

So if , then

[Somye]

Okay, so I used a Karnaugh diagram for this question, just to set out some of my work

I'm using ^ as intersection, because I can't find a good symbol on my keyboard

so, let Pr(P ^ Q) = x
therefore, Pr(P' ^ Q) = x

So, using our karnaugh diagram, we can see that Pr(Q) = 2x

So, Pr(P) * Pr(Q) = Pr(P ^ Q) for independent events

So Pr(P) * 2x = x
and it follows that Pr(P) = 1/2

[Lasercookie]

I'm using ^ as intersection, because I can't find a good symbol on my keyboard

The latex symbol for intersection is \cap (for union it's \cup). It's pretty effortless to convert what you had there to latex. You can pretty much just wrap each line of your maths there in [ tex ] [/tex ] tags (without the spaces). If you wanted, for the times you could use \times instead (or \cdot for just a centred dot), and for the fraction you'd need to do \frac{1}{2}.

[destain]

wow thanks, actually the simplest question with that explanation LOL, but didn't understand a single thing in the solutions

[BubbleWrapMan]

Even if these explanations are simpler, try to figure out the VCAA solutions using Venn diagrams or Karnaugh maps (if you have time)