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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 does the probability theory apply to statistics?

Statistics is the study of how probable an observed event is under a set of assumptions about the underlying probability distribution.

How many different ways can you arrange the word This?

Since the letters of the word THIS do not repeat each other, the number of different ways you can arrange them is simply the number of permutations of 4 things taken 4 at a time, or 4 factorial, or 24.

No, I'm not going to list them, because that would trip Dingo-Bot for profanity. But you knew that, didn't you?

How do you do probability with dice?

Roll the dice and if you're doing to put it with fractions the denominator is 6

What is the probability of obtaining getting a number greater than 4 when rolling a single die once?

Since there are two numbers greater than 4 on a six sided die (5 & 6), the numerator of your fraction is 2. There are six possibilities in total (1, 2, 3, 4, 5,6), so that's your denominator. Your fraction will end up being 2/6, simplified it will be 1/3 or 1 out of 3.

How do you test the normality of a random variable?

There are various goodness-of-fit tests. The chi-square and Kolmogorov-Smirnoff tests are two of the better known of these.

What is the probability of obtaining a sample proportion of red M and M's greater than 0.165 from a sample of size 400 from this population?

You would REALLY first need to find out what percentage of M&Ms are red. Since the sample is quite large, if this base percentage (as a ratio) is quite a bit lower than 0.165, then the probability you ask for is almost zero; if the ratio is quite a bit larger than 0.165, the probability you ask for will be almost 1 (i.e., 100%); only if the base probability is very close to 0.165 would you get more "interesting" results.

What do you do if none of the conditions of using a z-score or the conditions for using a t-score are met?

If we are testing a hypothesis about the population mean , if none of the conditions of using a z-score or the conditions for using a t-score are met, we may use a proper non-parametric test.

How many people have birthday on nov 11 2011?

None, since, as of nov 4, 2011, nov 11, 2011 has not yet occurred.

What do you know about 2 dice being rolled?

You know that the sample space of one die being rolled is

{1,2,3,4,5,6}, if you roll two dice,

you have a sample space with 36 elements. Here it is: (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

From this we can calculate many probabilities. We could look at the sums. For example what is the probability of rolling two dice and have a sum of 2?

There is only one way out of 36 for this to happen so it is 1/36.

Similarly, what is the chance of rolling a 1 and a 3, in either order?

What is the chance of having a sum of 6? All these answers come directly from

the sample space above.

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