5

Suppose that A and B are independent events such that P (4) = 0.20 and P(B) = 0.70_ Find P(4 n B) and P(4 U B). (If necessary, consult list_of formulas: )P(4 n B) =...

Question

Suppose that A and B are independent events such that P (4) = 0.20 and P(B) = 0.70_ Find P(4 n B) and P(4 U B). (If necessary, consult list_of formulas: )P(4 n B) = P(4 U B) = 0

Suppose that A and B are independent events such that P (4) = 0.20 and P(B) = 0.70_ Find P(4 n B) and P(4 U B). (If necessary, consult list_of formulas: ) P(4 n B) = P(4 U B) = 0



Answers

Interpretation Suppose you are a hospital manager and have been told that there is no need to worry that respirator monitoring equipment might fail because the probability any one monitor will fail is only $0.01$. The hospital has 20 such monitors and they work independently. Should you be more concerned about the probability that exactly one of the 20 monitors fails, or that at least one fails? Explain.

In this question, we're told that the probability of a is no 0.7 on the problem it'd be is no point fall. And we're told these two events are independent and we asked, Find policy of a be the owners short 100 Andi. So because their independent this is quite a simple question. Whole minutes Dude is poverty of ambi and cools probability of a times removed C b. And this is only the case if they are independent. So all we need to do, it's substrate. All of our visa appropriated A is no 0.7, and the probability of B is no point. Fall on that comes to North point to date and that we have to

For this question, we are told the probability of a It is not painful. The probability of a aunt may. There's no 0.5. We're also told that A and B are independent, which is important, and were then asked to find probability will be so because their independent we can use the prophecy of a on B equals probability of a times policy off big. I mean, to rearrange us to make probably be the subject to any to move property A to this side by division. So when we get a probability of a on B divided well, the probability of a ankles so busy Okay, consumption of I eat, you get 0 00.5 over. No point for is probability of being No, this actually comes out 1.25 which is an impossible answer. As in pictures that I am, we probably aren't independent or because you could never have problems

In this question we are given with some data and then we have to find the probability of B. Or we can say that we have to find the value of B. Okay, so first of all, I'm going to write given data or given information that is for ability of AIDS 0.4 probability of A plus B. Or we can say that Probability of a Union B is 0.7 and probability of B is it was to be okay. And we have to calculate this big for two conditions. In the first condition, it is told that if the events are made you exclusive, okay, You know that the events are militarily exclusive, then the probability of a intersection B is equals to zero. So due to this reason now you can say that they have to apply the formula probability of A and B. That is close to the probability of a less probability of being. And we have to put here all the values probability of a human being is 0.7 probability of a 0.4 probability of B. S. P. And from here we get the value of P. That is 0.3. Okay. This is the answer for the first question and now we move on the second question. In the second part, it is told that the event uh independent. Okay. So due to the reason that the the events are independent, we know that probability of the intersection. B can be written as probability of it into probability of B. So due to this reason, I can say that now I'm going to apply the addition formula that is for a variety of the evening. It was two probability less probable baby minus probability they interception. And now I put that will work the intersection big. So I get here the union D equals two E. A. Let's baby minus see A. Into B. B. Now I replace here all the values But over the pain and being 0.7 probability of pain. A data point for probability of B. S. C. And minus whatever the deal is. 0.4 Probability of B. S. Okay. Now from here we have to make the calculations so you can see that we can Subject zero Point Forward. So the 30 year 0.3 is it goes to T -0.4 weeks. That is the question of 160 Around me. Or if I divide by 0.6 Then I get the value of peace. That is 0.3. The world was 0.6 that it was too one x 2. Or we can say that 0.5. So we got the value of that is 0.5 in the second case. Okay So here are the answers in the first part, We got paid goes to 0.3, and in the second one we got pretty close to 0.5. Okay, thank you.

This problem requires us to use a multiplication rule when two events and be our independent, the probability that both occur. So the probability that a and B occur is the probability of a multiplied by the probability of B and this problem. We're told that the probability of A and B occurring is 0.13 and the probability of a occurring is for tense. We're looking for the probability of B solving this algebraic lee. If I divide both sides by 0.4, I'll find that the probabilities that be occurs is 0.3 to 5.


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