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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
How many six are in a deck of cards?
4:
6 of Spades
6 of Diamonds
6 of Hearts
6 of Clovers
Four (4). One of each suit.
What is the probability of rolling a multiple of 2 on a six sided die?
Assuming an unbiased die, there are six possible outcomes with equal probability {1, 2, 3, 4, 5, 6}. Of these six possibilities three of them, namely {2, 4, 6}, are divisible by 2.
Probability = number_of_successful_outcomes/total_number_of_outcomes
= 3/6
= 1/2
It is 0.3857
What are the odds of rolling any three pair of numbers using 6 dice?
The odds of rolling any number in one roll of one die is 1 in 1. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll is 1 in 1 times 1 in 6, or 1 in 6.
Now, look at the second pair of dice. The odds of rolling any number other than a number on the first pair is 5 in 6. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll, not the pair in the first roll is 5 in 6 times 1 in 6, or 5 in 36.
Now, look at the third pair of dice. The odds of rolling any number other than a number on the first two pairs is 4 in 6. The odds of rolling the same number in one roll of one die is 1 in 6. Each die is unrelated, so the odds of rolling a pair using two dice in one roll, not one of the first two pairs is 4 in 6 times 1 in 6, or 4 in 36.
To compute the total odds of rolling three pairs of numbers using 6 dice, simply multiply these odds together. That is 1 in 6 times 5 in 36 times 4 in 36, or 30 in 7776. Reducing that to lowest common fraction, you get 5 in 1296.
(This calculation assumes that the three pairs are different. If two or three of the pairs are allowed to be the same, the computation is different.)
Can the binomial distribution be normalized?
No.
I am using "normalization" as used in probability theory as application of a normalizing constant to a value, to make it conform to a certain distribution.
What are the odds of getting in a fight today?
it depends how hot-headed you are =P and how many people you associate with. and what people you associate with. and how hot-headed the people you associate with are. =P
What is the difference between probability distribution and probability density function?
A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.
What does to have in spades mean?
Something sb. has in spades means Sb. has plenty ofsomething. Ex: They had financial trouble in spades.
What is the probability of picking a jack from a pack of playing cards?
In a full deck of 52 cards your chances are one in thirteen. The same goes for every other card as well not just jacks.
The number of combinations - not to be confused with the number of permutations - is 2*21 = 42.
Red, blue, green or yellow.
Red, blue, green or yellow.
Red, blue, green or yellow.
Red, blue, green or yellow.
Can someone be sweet and cool at the same time?
No absolutely not. They are mutually exclusive. One cannot be sweet if one is cool because being cool demands a certain level of menace which sweet cannot possibly provide. One cannot be cool if one is sweet because people don't like other people to be sweet and hence they'd be unpopular
Two events are mutually exclusive if the occurrence of one depends on the occurrence of the other?
That depends on your definition of "depends." Mutually exclusive events are events that cannot occur at the same time. If you knew that Independent events most certainly can happen at the same time, you could easily deduce that mutually exclusive events are always dependent events. And while it's true dependent events affect the outcome of one another, that's not so easy to see when your dealing with events that don't occur in succession.
It can be said that if a mutually exclusive event occurs, the other events that are mutually exclusive in relation to it have not taken place, i.e. the complement of that event has not taken place. When you look at only two events that are mutually exclusive and jointly exhaustive (i.e. all the possible events) like flipping a coin once and getting either a head or a tails (where the probability of the coin landing on it's side is 0), you can say that one event, flipping a head, is dependent on the other event, flipping a tail, not happening. Therefore the events are mutually exclusive.
Now imagine two events which are still mutually exclusive but not jointly exhaustive, e.g. rolling a 2 or a 3 with a six sided die. Lets assume the die is not weighted so the probability of each is 1/6. A roll of two does not only depend on not rolling a three. To roll a 2 means not rolling a 1,3,4,5 or 6. To say that rolling a 2 and rolling a 3 are mutually exclusive if the occurrence one depends on the occurrence of the other is ambiguous at best, if not wrong. Rolling a 2 and rolling a 3 are mutually exclusive only because its impossible for both to happen at the same time with one roll, or you can say that P(2and3)=0.
It's fair to say that two events are mutually exclusive if the occurrence of one depends on the other not happening. But if you thought that two events are mutually exclusive because the occurrence of one relays on the occurrence of the other then you were wrong. That just describes dependent events in succession.
If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannot occur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event. If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannotoccur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event. If one event's occurence depends upon the occurence of another, and the events cannot occur with a certain outcome otherwise, they are said to be dependent events. Mutually exclusive events are events that cannotoccur together, as the occurence of one prohibits the occurence of the other. An example of a mutually exclusive event is this: two dice are rolled; what is the possibility of rolling both a nine and a double? One cannot roll both a nine and a double simultaneously; therefore, the events are mutually exclusive because one outcome excludes the other. An example of a dependent event is this: Susan is baking cookies. She has enough batter for two dozen chocolate chip cookies and one dozen oatmeal cookies. Therefore, the ratio of chocolate chip to oatmeal is 1.5:1. If Susan's little brother eats half of the chocolate chip cookies, the ratio changes to become 1:1. The possibility of the ratio being 1:1 is dependent upon Susan's brother eating half of the chocolate chip cookies. Thus, it is a dependent event.
Mutually exclusive events refers to the events that cannot occur at the same time.
When is it necessary to use the Simplex method rather than the graphical method?
When you have 3 variables or more. In paper, we can only draw 2 dimensional shapes.
How many ways can an IRS auditor select 3 of 11 tax returns for an audit?
39916800/241920=165 would be the math answer.
How do you do permutations with repeating symbols?
Suppose you have n objects and within those, there arem1 objects of kind 1
m2 objects of kind 2
and so on.
Then the number of permutations of the n objects is n!/[m1!* m2!...]
For example, permutations of the word "banana"
n = 6
there are 3 "a"s so m1 = 3
there are 2 "n"s so m2 = 2
therefore, the number of permutations = 6!/(3!*2!) = 720/(3*2) = 120.
What is the independent and dependent event for if you pull two pair of socks at the same time?
The independent event is the first pair of socks. The dependent event is the second pair of socks, because the first pair changes the probability of the second pair.
Yes, the question said "at the same time", but this answer remains valid because one pair will affect the other pair, somehow, someway, i.e. even if you choose both pairs "in the blind", they are mutually interdependent. That's the real answer.
What is the independent and dependent event for pulling two marbles out of a bag?
The first marble is the independent event because its probability is only based on the sample space of the bag. The second marble is the dependent event because its probability is based on the sample space of the bag which has now been changed by the first marble.
The chance of a pin landing with the sharp point facing up would depend on multiple factors such as how the pin was dropped, the surface it was dropped on, and its shape/weight distribution. It is generally difficult to calculate an exact probability due to these variables.
