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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
What are the requirements for probability distribution?
(1) That the probabilities lie between 0 and 1.
(2) The sum of all probabilities of the distribution sum up to 1.
How many ways can you arrange the letters PARTY if the first letter must be an A?
The number of arrangements of the letters PARTY, if the first letter must be an A is the same as the number of arrangements of the letters PRTY, and that is 4 factorial, or 24.
Is it true that the probability of rolling a six with a fair die five times in a row is?
The probability of rolling a six with a standard die five times in a row is (1 in 6)5 which equals 1 in 7776 or about 0.0001286.
How many arrangements can be made with the letters sociological?
There are 12 factorial or 479,001,600 permutations of the letters in the word SOCIOLOGICAL. However, since the letter O occurs three times, the letter I occurs twice, the letter L occurs twice, and the letter C occurs twice, you have to divide that by 8 (O), 2 (I), 2 (L), and 2 (C) giving you 7,484,400 distinctpermutations.
What is the probability that 14 rolls of a fair die will show 6 ones?
When a die is rolled once, the probability of 1 showing up is 1/6 .
When a die is rolled 14 times, the probability of 1 showing up 6 times is a binomial probability.
Let x = number of times 1 shows up
P(x=6) = 14C6 (1/6)^6 (5/6)^(14-6)
= 14C6 (1/6)^6 (5/6)^8 = 0.014982
The probability distribution is
P(X = 1) = 1/36
P(X = 2) = 3/36
P(X = 3) = 5/36
P(X = 4) = 7/36
P(X = 5) = 9/36
P(X = 6) = 11/36
P = 0 otherwise.
Mean(X) = 4.4722
Variance = 1.9715
The answer depends on what the standard deviation is.
What is the difference between poisson and binomial distribution?
Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution.
Binomial is the most preliminary distribution to encounter probability and statistical problems.
On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
When rolling 2-six sided number cubes what is the probability of rolling a nine?
There are 36 permutations of two standard dice. Of these, four have a sum of nine, specifically 3+6, 4+5, 5+4, and 6+3. The probability, then, of rolling a nine on a pair of standard dice is 4 in 36, or 1 in 9, or about 0.1111.
It is impossible to determine the percentiles if you are given only the sample mean since percentiles are a measure of the spread of the data; the mean gives no information on that.
How many different telephone numbers of 7 digits can be formed if the first cannot be zero?
There are a number of issues with this question. Phone numbers are limited to more than just the first number not being 0. What about 9-1-1? What about 4-1-1, or 5-1-1, or 3-1-1? What about 1-Area-Number? What about 1-0-Carrier-country-1-city-number? What about the fact that some exchanges do not permit a 0 or a 1 as the second digit of the number? What about the fact that the sum of the first and third digits are constrained to not be certain sums? (The last two rules are to prevent older rule-base auto-long-distance dialing detection logic from misdetecting an area code.) What about constraints on the last four digits.
With that said, and with only the constraints imposed by the question, i.e. ignoring these other known constraints, there are 9,000,000 different phone numbers in one exchange.
What is the experimental probability of rolling an even number?
The experimental probability of anything cannot be answered without doing it, because that is what experimental probability is - the probability that results from conducting an experiment, a posteri. This is different than theoretical probability, which can be computed a priori. For instance, the theoretical probability of rolling an even number is 3 in 6, or 1 in 2, or 0.5, but the experimental probability changes every time you run the experiment.
Which comes up more when flipping a quarter Heads or tails?
Neither. Its a 50:50 probability. In the long run, heads will match tails.
What is the difference between population and sample distribution?
Sampling distribution is the probability distribution of a given sample statistic.
For example, the sample mean. We could take many samples of size k and look at the mean of each of those. The means would form a distribution and that distribution has a mean, a variance and standard deviation.
Now the population only has one mean, so we can't do this.
Population distribution can refer to how some quality of the population is distributed among the population.
How many different five-letter initials with none of the letters repeated can people have?
There are 26*25*24*23*22 = 7,893,600 sets of initials.
When two dice are rolled what is the probability that both will not be the same number?
The are 36 permutations of two dice. Of these, 6 permutations have the two dice with the same number, specifically 1+1, 2+2, 3+3, 4+4, 5+5, and 6+6. The probability, then, that two dice rolled will not have the same number is 30 in 36, or 5 in 6, or about 0.8333.
What is the probability you will select a girl from the class if you have 17 girls and 10 boys?
Oh, dude, let me break it down for you. So, if you have 17 girls and 10 boys in the class, the probability of selecting a girl is like the number of girls divided by the total number of students. So, it's 17 girls out of 27 students, which simplifies to about 63%. Cool, right?
What proportion of a normal distribution is located in the tail beyond z 2.00?
Pr(Z > 2.00) = 0.02275
There are many sites that will enable you to do this quickly and simply. However, some give Pr(Z < z), others give Pr(Z > x) or Pr(0 < Z < z). These are all simply related since if
Pr(Z < z) = p, then
Pr(Z > x) = 1 - p, and
Pr(0 < Z < z) = p - 0.5
Make sure you know which one the site is using.
In Excel, the function NORMSDIST(2.00) will return 0.97725 = Pr(Z < 2.00), or 1 minus the required number.
I use the one given in the link which gives Pr(Z > z).
How do you prepare for probability and queueing theory arrear exam?
Try to understand the subject. If in doubt ask someone to explain. Study the topics and try out plenty of past examination papers.
When the population standard deviation is not known the sampling distribution is a?
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
