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Question 5 Not yet answeredIf A and B are two events with P(A) 0.60,P(B / A)=0.35. P(AUB) =0.69 Then P(BC)Marked out of 2.00...

Question

Question 5 Not yet answeredIf A and B are two events with P(A) 0.60,P(B / A)=0.35. P(AUB) =0.69 Then P(BC)Marked out of 2.00

Question 5 Not yet answered If A and B are two events with P(A) 0.60,P(B / A)=0.35. P(AUB) =0.69 Then P(BC) Marked out of 2.00



Answers

$\mathrm{A}$ and $\mathrm{B}$ are events such that $\mathrm{P}(\mathrm{A})=0.42, \mathrm{P}(\mathrm{B})=0.48$ and $\mathrm{P}(\mathrm{A}$ and $\mathrm{B})=0.16$. Determine (i) $\mathrm{P}(\operatorname{not} \mathrm{A}), \quad$ (ii) $\mathrm{P}(\operatorname{not} \mathrm{B})$ and (iii) $\mathrm{P}(\mathrm{A}$ or $\mathrm{B})$

So in this problem and part A, I need to find what is the probability, right? The probability of event be happening. So I know I know that the probability of a or be happening and the probability of even a happening So what I can do is doing the opposite of what addition? Role to make do. I'm just going to subtract the probability of a happening because I know that when we do addition role to, we're adding both the events of a and the event off B and then subtracting any overlaps. But here I don't know be so I need to subtract a in order to know what I got left, which is be so let's see so probability. So I subtract this. So in other words, I got 0.6 5653 thousands minus the events of A which is 0.392 and that should give me that. You give me 0.261 and there we go. We have part A which is that probability of event be happening. It's 261 now. Part B part B of this exercise is to find the probability of not a of not a so dear. The way to do this is that I already know what is the additional number to write A or B. They went either a happening or be happening, so I know that zero point sits under 53 minus anything that it's not a so in order to find anything that is not a have to subtract a right out of bad probability. So 392 and if you can see it's the same s event A as in a part a of this exercise. So I end up with the probability of 0.261 and that's our party. And now last book, but not least, huh? We're gonna work with Part C, which is the probability of A and B, and here's a little tip. So if they are mutually exclusive, what is the probability of A and B happening together? Well, that's easy. Zero

In this example, we're told that there's mutually exclusive events and these mutually exclusive means they basically don't intersect at all. So we have event A. And event peak Probability of 8.17 And probability of fi is .32. So basically here the probability of a intersect with peas equals to zero. So for mutually exclusive events, the probability of here given B is basically property of the intersection B. Over the probability of B, which is zero. And same thing probability of the given. Okay, it's basically a probability of B intersect with over probability of A, which is also zero. So and service zero.

You know that probability of A. When B has been occurred is given by probability of a intersection B divide probability of B. From here, I can write probability of B. Multiply probability of A. N. B has been occurred will be equal to the probability of a intersection. This is intersection. The intersection be similarly, if I write probability of a multiply, the probability of B. When A has been occurred will be equal to probability of B intersection A. We know that a intersection B is equal to be intersection the intersection. A probability of a intersection B is equal to probability of B intersection C. So I can write from let's suppose this is equation for us, this is equation second, I can write that B. B multiply P. A by B will be equal to be a multiply B. Be by A. So in the questions we are the one, the values which are We need to find PBPA bi big is given as one x 2, one x 4. Multiply two x 3. So from here B B can be written as one x 3. So option one x 3, option B is going to be the right answer.

In this problem. Contact the of a. Yes, nothing but one minus we have a compliment which comes as one minus 10.3 which is 0.7 B. B. Is 0.4. Now we know that. Yeah. Yes the the intersection B. Yes B. The intersection the compliment rooms 0.7. Is he close to be the intersection B less. She is .5. Or we get be a intersection? Be us 0.2 B. Hey union the compliment is here. Yes be complement minus B. The intersection. The compliment common sense 0.7 Plus this is 1 -14 which is .6 minus foreign place. This comes as pointed. Next we have B. Be given a union. The compliment as the me intersection. A union we complement divided by Mhm. A union. The compliment now from secretary now from the secretary B. In in the section A union me compliment. There's nothing but be in the section A union the intersection, the Complement The intersection we complemented zero. So this comes as the intersection. A. So they required probability required probability sp the intersection B divided by be a union. The compliment just point to buy pointed. Just one of us correct option is that's


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