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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

Why 1 is one and 2 is two?

They are simply convenient notations. In fact, in binary, 10 is two.

What is the probability of when you roll a dice you will get a higher number than the number you got the last you rolled the dice?

5/12

Consider the possibile outcome of two rolls of a die (where order matters):

(1,1)

(1,2)

(1,3)

.

.

.

(4,6)

(5,6)

(6,6)

There are 6*6=36 possible outcomes. Of these, the following would achieve the result desired:

(1,2)

(1,3)

(1,4)

(1,5)

(1,6)

(2,3)

(2,4)

(2,5)

(2,6)

.

.

.

(5,6)

For the first die equal to 1, there are 5 successful results. For the first die equal to 2, there are 4 successful results....For the first die equal to 5, there is 1 successful result. The total number of successful outcomes=5+4+3+2+1.

So the probability that the desired outcome is obtained=(5+4+3+2+1)/36=15/36=5/12.

A standard dice is rolled 10 times withthe out come 2 1 3 2 5 1 0 in this order you can you make it where it is less or equal to 8?

The lowest number I can roll on a die is 1.

In ten rolls, that's a minimum of ten; I cannot make it 8 or less.

Zero is a foul throw.

Solutionsn of Moment-generating functions?

Your question did not identify one distribution in particular. I have provide in the related link the moment generating functions of various probability distributions.

What is the relevance of probability and statistics in the field of information technology?

In the field of IT you are dealing with probabilities all day long. How long will the hardware last, how can you keep the signal for the network strong all over the building, how will adding a new group of computers impact the network, or heaven forbid your network come under attack and you need to keep damage to a minimum while fending off the attack. IT professionals think in probabilities. They're always running scenarios through their heads to come up with and fix problems before they occur.

Why would someone want to assume that your sample data represents a population distrubution?

Most people take samples so that they may make estimates of parameters of interest: mean, variance, etc for the whole population. For such an estimate to have any validity the sample data must be assumed to represent a population distribution. Otherwise any conclusions based on the sample are valid only for the sample: hardly worth the effort!

What is the probabilitly of rolling a 4 on a 10-sided dice?

The probability is (0.1) times (the number of faces with '4' marked on them).

Flip a coin 10 times tails on the 10th?

The result of the tenth toss is usually independent of the previous nine so the probability is 0.5.

What is the probability that a card is both a club and queen?

One in 52 - because there are 52 cars in a deck, and only one Queen of Clubs.