# events

1. ### Probability: events selected from unit interval

Hi I'm having trouble determining which events this question is referring to maybe this wording makes more sense to you than it does to me. A number U is selected from the unit interval. Let the events A and B be A= U differs from 1/2 by more than 1/4 and B=1-U is less than 1/2. Find the...
2. ### Mutually Exclusive Events

Hello, If we denote P(A)=0.2 and P(B)=0.2 , then is it that we seek P(A^c \cap B^c)=0?. The answer solution says 0.6. Who is wrong here? Thank you!
3. ### Contingency and the intersection of two events.

Hi everybody, Here is my problem: I am being asked to solve P(R|C). C=number of patients who have completed treatment, and R=number of return patients. However, my understanding is that I need to know the intersection of P(C) and P(R) in order to solve P(R|C). But, to solve for the...
4. ### Limit relation for events

Let (\Omega,\mathcal F,P) be a probability space and (A_n)_{n\ge1} be a sequence of events in \mathcal F. Prove that {{I}_{\underset{n\to \infty }{\mathop{\underline{\lim }}}\,{{A}_{n}}}}+\underset{n\to \infty }{\mathop{\overline{\lim }}}\,{{I}_{A_{n}^{c}}}=1. (Rock)
5. ### Probability: Independent Events

Suppose that the probability a child is male is p and the probability the child is female is 1 - p. We choose four children at random. Let A be the event that there is at most one girl and B the event that there are children of both sexes. Show that there is a value of p for which A and B are...
6. ### probability of conditional events

can someone show me how to do second part and third part please? i really have no idea how to start it.
7. ### probability of independent events

i have drawn the venn diagram for the question... i am not sure it's correct or not. the question states both are independent events. i dont understand the working in part b ... for me , my ans would be p(A) +p(B).. correct me if i am wrong. thanks in advance.
8. ### Let A,B be two events such that P(A) = .4 ; P(A U B)= .7. Let P(B)= p

Let A,B be two events such that P(A) = .4 ; P(A U B)= .7. Let P(B)= p a.) For what choice of p are A and B mutually exclusive events? b.) For what choice of p are A and B independent events? I know P(A U B) = P(A) + P(B) - P(A ∩ B) thus P(A ∩ B) = 0.4 + P(B)-0.7 but I don't know how I would...
9. ### Probability Question. Events A and B....

The question goes like this: The events A and B are such that P(A)=0.6, P(B)=0.3 and P(A|B)=0.2. Find the probability that (i) both A and B occur, (ii) at least one of A and B occurs, (iii) exactly one of A and B occurs. I'm fine with part (i) but have no idea how to go about solving (ii) and...
10. ### Test the Pair of Events for Independence

A B C Total D 0.18 0.12 0.00 0.30 E 0.42 0.28 0.00 0.70 Totals 0.60 0.40 0.00 1.00 Are the events C and E independent? I know the answer is no, not how are they not independent? I've been struggling a bit with probability and cannot seem to figure this out.
11. ### Probability Independent Events

Hi guys, I'm stuck on these 2 questions, but I think that once I can do the first, the other should be reasonably straightforward. I would really appreciate some help. I've attached a png if it's easier to read. Thanks!
12. ### Probabilty theory - question about two independent events

If two events A and B are mutually exclusive (A\cap B=\phi ), then A and B are dependent. It implies that if A and B are independent, they are not mutually exclusive. Is it true that if A and B are independent, then either A\subseteq B or B\subseteq A?
13. ### Probability of dependent events

So I've got this problem: From a group of 10 people (4 women and 6 men) 5 will be chosen randomly to occupy the following places in a committee: 1 president 1 vicepresident 3 council representatives 1. If 3 men were chosen to occupy the last 3 places in the committee, how many different...
14. ### How can we condition on events with probability 0?

We are given that the joint density of X and Y is f(x,y) = \begin{cases} & .5 \; \text{if } \; 0 \leq x \leq .5 \; \;\text{and}\; 0 \leq y \leq .5 \\ & 1.25 \; \text{if } \; 0 \leq x \leq .5 \; \;\text{and}\; .5 \leq y \leq 1 \\ & 1.5 \; \text{if} \; .5 \leq x \leq 1 \; \;\text{and}\; 0 \leq y...
15. ### Mutually Exclusive Events in Probability

Consider a Stanley Cup playoff series in which the Toronto Male Leafs hockey team faces the Ottawa senators. Toronto hosts the first, second and if needed, fifth and seventh games in the best-of-seven contest. The Leafs have a %65 chance of beating the Senators at home in the first game. After...
16. ### Probability of Independent Events: showing abstractly that two events are independent

I haven't had a proofs class, so proofs always seem so complex to me. Here's the question: If A,B, and C are mutually independent, show that the following pairs of events are independent: A' and (B and C') (I understood the other ones). Also show that A', B', and C' are mutually independent...
17. ### finding combinations for dependent events with restricted picks from the sample space

I'm programming something for a text based game that I play and I've got a problem that I've been working on for a while and just about to just brute force it, but before I do I'm hoping someone has a solution. In my game you can get afflictions and to cure theses afflictions there are a number...
18. ### probability of Independent events help.

The probability of any unrelated events occurring together in the same period. Now for the Mathematical probability of these events happening independently of each other. Here is the logic. If each event above is considered as an event on its own and not related to another event mentioned...
19. ### odds of independent events

Forgive me, I read through that entire sticky post at the top, and at the end, if anything, I was more confused. So I'll spell everything out here, and if one of you fine talented folk can tell me if I'm on the right track or not you will make my day! I have ten cards turned face down. One has...
20. ### showing that two events are dependent/independent

If we have a table for two types of company which have either high or low risk sock given thus: COMPANY TYPE LOW RISK HIGH RISK Internet services .....6 ...............9 Financial Service .....20 ..............5 and we want to see if the company type is dependent or independent of the...