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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 different ways can you arrange 5 out of 7 books on a book shelf?
There are only 5 places on the shelf. You have 7 books to choose from. We will ignore the order of the books on the shelf. The first place can be filled from a choice of 7 books, the next place from 6, the next place from 5, the next from 4, and the last of the 5 places from 3 books.
So the number of ways of choosing the 5 is found from 7 * 6 * 5 * 4 * 3 = 2520
How many permutations are in the word mathematics?
The word MATHEMATICS has 11 letters. The number of permutations of 11 things taken 11 at a time is 11 factorial (11!), or 39,916,800.
What is the probability of picking a prime number from numbers between 1 and 20?
The probability is 8/20.
1/3.
Indeed, there were four answers you had to choose from. If one is eliminated as you know it is definitely wrong, then you are left with three possible answers, one of which is correct. Thus you have 1 correct answer out of three possible, and the probability to randomly pick the correct one is 1 out of 3, or 1/3 or 33.333 %
The question contradicts itself. The order of the letters is irrelevant in a combination [though it does matter in a permutation]. So what is it that you are asking for? Combinations or order-dependent arrangements?
What is the probability that all of the children in a family of five children will be boys?
The genders of children within the same family are not independent. So the answer will depends on the pattern of children's gender in the family's ancestry, as well as the age of the parents.
However, if you make the unreasonable and unjustified assumption that the genders are independent and that the probability of either gender is 1/2, then the answer is (1/2)5 = 1/32.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
What is the probability you'll get a king express as fractions?
The answer will depend on
- the deck of cards that you draw from: a pinochle deck, a deck with jokers, etc;
- how many cards are drawn,
- if more than one card is drawn, whether or not a drawn card is replaced before the next one is drawn.
Historical events which have occurred have a probability of 1. They are a certainty. This refers to the event itself, not some historian's or politician's interpretation of what happened. However, the probability that they will occur again depends on the event. Exact recurrence is impossible (probability = 0).
Which sampling method is based on probability?
There are many such methods: cluster sampling, stratified random sampling, simple random sampling.Their usefulness depends on the circumstances.
What is sampling distribution of the mean?
Thanks to the Central Limit Theorem, the sampling distribution of the mean is Gaussian (normal) whose mean is the population mean and whose standard deviation is the sample standard error.
What is the ratio of favorable outcomes to total outcomes?
The probability of the event that comprises the favourable outcome.
How does sample size affect the size of your standard error?
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
The standard error should decrease as the sample size increases. For larger samples, the standard error is inversely proportional to the square root of the sample size.
What is the probability of rolling either a 5 or 6 or 8 or 9 before rolling a 7 with two dice?
Consider the three events:
A = rolling 5, 6, 8 or 9.
B = rolling 7
C = rolling any other number.
Let P be the probability of these events in one roll of a pair of dice.
Then P(A) = P(5) + P(6) + P(8) + P(9) = 18/36 = 1/2
P(B) = P(7) = 6/36 = 1/6
and P(C) = 1 - [P(A) + P(B)] = 1/3
Now P(A before B) = P(A or C followed by A before B)
= P(A) + P(C)*P(A before B)
= 1/2 + 1/3*P(A before B)
That is, P(A before B) = 1/2 + 1/3*P(A before B)
or 2/3*P(A before B) = 1/2
so that P(A before B) = 1/2*3/2 = 3/4
How many possible ways to arrange the word Mississippi?
Nonew, since mississipi is not a word!
Nonew, since mississipi is not a word!
Nonew, since mississipi is not a word!
Nonew, since mississipi is not a word!
What z-score value separates the highest 40 percent of the scores from the rest of the distribution?
0.2533
What is the mean of a normal distribution?
It is the expected value of the distribution. It also happens to be the mode and median.
It is the expected value of the distribution. It also happens to be the mode and median.
It is the expected value of the distribution. It also happens to be the mode and median.
It is the expected value of the distribution. It also happens to be the mode and median.
That depends.
Picking a red ball is 4/9
Picking a green ball is 3/9 = 1/3
Picking a yellow ball is 2/9.
Picking a ball is 9/9 or 1 because you'll always take one.
How many different ways can you rearrange the letters of the word 'chocolate'?
Make notes that:
- There are 2 c's in the given word.
- There are 2 o's in the given word.
Since repetition is restricted when rearranging the letters, we need to divide the total number of ways of rearranging the letters by 2!2!. Since there are 9 letters in the word to rearrange, we have 9!. Therefore, there are 9!/(2!2!) ways to rearrange the letters of the word 'chocolate'.
We select 1 shirt out of 6 shirts in (6 choose 1) ways or 6 ways. Then, we select 1 out of 3 pairs of shorts in (3 choose 1) or 3 ways. Therefore, the possible combinations of a shirt and a pair of shorts is 6 * 3 = 18 possible combinations.
How likely is it for an event to happen written as a percentage?
100 times its probability.
100 times its probability.
100 times its probability.
100 times its probability.
