# events

1. ### Events in a row within some arbitrary n.

Okay, so say for example, at a football (soccer) game, the chance that someone walking through the turnstiles is an away fan, is 0.1 and 0.9 that they are a supporter of the home team. Now I observe 100 people walking through the turnstiles. How would I calculate the probability, of, within...
2. ### Expressing events

I am given three events; E, F and G. I need to express the following, in terms of their events and complements; - At least one of E, F and G How do i go about doing this? I seem to get a really long expression, but there must be a short way of going about it.
3. ### Independent events

I am confused.. It doesn’t seem to be true that P(A and B) for two events happening consecutively is the same as P(A and B) for two events happening simultaneously. So we should never use the notation P(A ∩ B), the probability of the intersection of A and B for the first case? (I have...
4. ### Probability of the union of independent events proof (induction argument)

I am trying to prove the following: If E_1, E_2, ... , E_n are mutually independent events, then P(E_1 \cup E_2 \cup ... \cup E_n) = 1 - \Pi^{n}_{i=1} [1 - P(E_i)| This is true for n=2 P(E_1 \cup E_2) = 1 - P(E_1^{C} \cap E_2^{C}) by DeMorgan's Law and since E_1 and E_2 are...
5. ### Independent events

I am given that P(A) >0, P(B) >0, P(C) > 0 (strictly greater) and P(B)P(C) = \frac{P(B \cap C)P(A \cap B)}{P(A \cap (B \cap C))} + \frac{P(B \cap C^{C})P(A \cap B)P(C)}{P(A \cap (B \cap C^{C})P(C^{C})} I am to deduce whether B and C could be independent. I am thinking no. In order for the...
6. ### Events A,B (independent, mutually exclusive), Help!

P(A/B)=0.2 , P(A/B^)=0.3 and P(B)=0.8 a) Are the events A, B independent ? b) Are the events A, B mutually exclusive ? Can someone solve this exercise please ? (Worried)
7. ### Complement Proof of independent events

If A and B are independent events, show that \bar{A} \ \ \text{and} \ \ \bar{B} are independent. I haven't a clue what to do for this one.
8. ### Probability of the Union of 4 events

What is the probability of the union of 4 events? The events are: E- hitting an even number on a dartboard= .0249 D- hitting a double P=.1049 N- hitting a number higher than 10 P=.0249 B- hitting a bullseye P= .007 I came up with: 1. P(E)+P(D)+P(N)+P(B) - 2. [P (E \cap D)...
9. ### probabilty of mutually exclusive events and trouble with understanding notation

Question. Consider three mutually exclusive and exhaustive events A_0, A_1 and A_2 where P(A_0\cup{A_1})=p_0 P(A_1\cup{A_2})=p_1 P(A_2\cup{A_0})=p_2. What condition on p_0, p_1, p_2 must hold? Now generalise to n mutually exclusive and exhaustive events A_0,...A_{n-1} where...
10. ### Mathematical symbols representing probability events

A number of multiple choice questions which I am working on relate to mathematical symbols which represent probability events…in order to tackle the questions, I need to be clear what is/ is not a valid mathematical symbol…. Are a, b, c, d (see below) valid mathematical symbols which can be...
11. ### Independence of two Events imlies independence of indicator variables

Hi everyone, I am trying to prove that events A1 , A2 are independent if and only if the corresponding indicator variables 1A1 , 1A2 are independent. I am a little bit clueless where to start, could someone give me a hint? Fontana
12. ### Independent Events

We flip a coin n times (n ≥ 1). For which values of n are the following pairs of events independent? (a) The first coin flip was heads; the number of all heads was even. (b) The first coin flip was heads; the number of all heads was more than the number of tails. (c) The number of heads was...
13. ### Probability with mutually exclusive events

Let S be the sample space of a repeatable experiment. Let A and B be the mutually exclusive events of S. Prove that in independent trials of this experiment, the even A occurs before the event B with probability P(A) / [P(A) + P(B)]. Having trouble showing that this is true. Any help is...
14. ### Mutuallly exclusive events

John and his friend plan to travel to North Dakota during winter break. The probability that they go by car is 2/3 and the probability that they go by plane is 1/5. What is the probability that they go to Florida by car or plane? These are independent events so P(A)+P(B) 2/3 + 1/5 = 13/15??
15. ### Mutually/ NonMutually Exclusive events

I'm still confuse about these events. Also 180 + 160 is more than 300. Where have I made the mistake? The owners of a music store placed ads in the newspaper and on TV advertising their annual 40% sale. They did a survey of the first 300 customers, and discovered that 180 saw the ad on tv, 160...
16. ### Conditional probabilty; dependent and independent events

This is my first post to this forum. I feel it's time I gained a proper grasp on probabilty and statistics, so I've started working my way through a text book on the subject... I made it as far as page 7! P(B|A) is the probabilty of B given that A is true. I understand that to mean that the...
17. ### Prove or Disprove Probability of Events

Let S be a well defined sample space where E, F and G are events. It is the case that Pr( E U F ∩ G)= 1- Pr(E' ∩ F') - Pr(G' ∩ (E U F))
18. ### Non exclusive/exclusive events

The owners of a music store placed ads in the newspaper and on TV advertising their annual 40% sale. They did a survey of the first 300 customers, and discovered that 180 saw the ad on TV, 160 saw the ad in the newspaper, and 75 saw the ad on TV and in the newspaper. What is the probability that...
19. ### Non-mutually/mutually exclusive events

A card is taken form a deck of cards and then replaced. After the deck is shuffled a second card is taken from the deck. Calculate the following probabilities a. Both cards are diamonts or both are hearts P(A or B) = P(A) + P(B) - P(AandB) P(A) should be= P(1st card diamand)X P(2nd card...
20. ### Probability involving the intersection of dependent events (I think)

Cards are drawn from an ordinary deck of 52 cards one by one without replacement. What is the probability that no heart is drawn before the ace of spades is drawn? I can't figure out the probability of either event, much less the probability of the events happening together.
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