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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 experimental result differ from the theoretical in terms of accuracy?

Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.

Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.

Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.

Provided that the correct model is used, the theoretical probability is correct. The experimental probability tends towards the theoretical value as the number of trials increases.

What is the probability that the a dice 2 is drawn if the two dice total is 5?

The probability, when the 2-dice total is 5, that one of the two dice shows a two is 1/2. The probability that that die is selected is 1/4.

The probability, when the 2-dice total is 5, that one of the two dice shows a two is 1/2. The probability that that die is selected is 1/4.

The probability, when the 2-dice total is 5, that one of the two dice shows a two is 1/2. The probability that that die is selected is 1/4.

The probability, when the 2-dice total is 5, that one of the two dice shows a two is 1/2. The probability that that die is selected is 1/4.

What is the probability of flipping heads and rolling an odd number?

These would be independent events; therefore, we can multiply the probabilities of each of the two events.

Probability of flipping a head: 1/2

Probability of rolling an odd number with a single die: 1/6

Required probability : 1/2 x 1/6 = 1/12

How many different committees can be formed from 10 teachers and 30 students if the committee consists of 2 teachers and 2 students?

There are (10 x 9)/2 = 45 different possible pairs of 2 teachers. For each of these . . .

There are (30 x 29)/2 = 435 different possible pairs of students.

The total number of different committees that can be formed is (45 x 435) = 19,575 .

How do you see that the sampling distribution of the mean is normal?

According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.


The necessary requirements are shown in bold.



According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.


The necessary requirements are shown in bold.



According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.


The necessary requirements are shown in bold.



According to the Central Limit Theorem, the mean of a sufficiently large number of independent random variables which have a well defined mean and a well defined variance, is approximately normally distributed.


The necessary requirements are shown in bold.

What is the probability of getting an ace of hearts and a king of hearts from a regular deck of cards without jokers?

The answer depends on how many cards are drawn and whether or not they are replaced before the next card is drawn.

The answer depends on how many cards are drawn and whether or not they are replaced before the next card is drawn.

The answer depends on how many cards are drawn and whether or not they are replaced before the next card is drawn.

The answer depends on how many cards are drawn and whether or not they are replaced before the next card is drawn.

What is the probability of getting 4 red cards from a standard deck of 52 cards?

If you are picking a card and putting it back before picking the next, it would be 1/2 * 1/2 * 1/2 * 1/2 = 1/16

If you are not replacing the cards, it would be 26/52 * 25/51 * 24/50 * 23/49 = 358800 / 6497400, or approximately 5.5%.

How many ways word crisis arranged?

There are 6 letter in the word crisis so the answer seems to be 6! (6 factorial), but there are two 'i's and two 's's which are indistinguishable and each of which can be arranged in 2! ways. So:

number_of_ways = 6!/2!2!
= 180 ways.

How many different ways can you arrange the letters of the word Malayalam?

There are 9!/[2!*4!*2!] = 3780 if you treat M and m as equivalent. Otherwise, there are twice as many.

What is probability compliment?

"That was a good bet!", perhaps.

"That was a good bet!", perhaps.

"That was a good bet!", perhaps.

"That was a good bet!", perhaps.

What is the values of the skewdness and kurtosis coefficient for the normal distribution 0 and 3 respectively?

No.


Skewness is 0, but kurtosis is -3, not 3.



No.


Skewness is 0, but kurtosis is -3, not 3.



No.


Skewness is 0, but kurtosis is -3, not 3.



No.


Skewness is 0, but kurtosis is -3, not 3.

How many possible outcomes for normal distribution?

Infinitely many. The normal distribution is applicable to a continuous variable whose domain is the whole of the real numbers.



Infinitely many. The normal distribution is applicable to a continuous variable whose domain is the whole of the real numbers.



Infinitely many. The normal distribution is applicable to a continuous variable whose domain is the whole of the real numbers.



Infinitely many. The normal distribution is applicable to a continuous variable whose domain is the whole of the real numbers.

Why is calculating the standard deviation an important part of data analysis?

It is a measure of the spread of the results around their expected value.

It is a measure of the spread of the results around their expected value.

It is a measure of the spread of the results around their expected value.

It is a measure of the spread of the results around their expected value.

What proportion of a normal distribution is located between z-0.90 and z 0.90?

0.368 or 36.8%.

And you should specify that it is a standard normal distribution.

0.368 or 36.8%.

And you should specify that it is a standard normal distribution.

0.368 or 36.8%.

And you should specify that it is a standard normal distribution.

0.368 or 36.8%.

And you should specify that it is a standard normal distribution.

What is the probability of not geeting a queen in a well shuffled deck of 52 playing cards?

If only one card is selected the probability is 12/13.

If only one card is selected the probability is 12/13.

If only one card is selected the probability is 12/13.

If only one card is selected the probability is 12/13.

How do you find the z score of 12.5?

To find the Z score from the random variable you need the mean and variance of the rv.

To find the Z score from the random variable you need the mean and variance of the rv.

To find the Z score from the random variable you need the mean and variance of the rv.

To find the Z score from the random variable you need the mean and variance of the rv.

What are the differences between sampling error and sampling bias?

Sampling bias is a known or unknown selection of data to be examined in an audit.

There should be no bias if the sample is random.

Ex ... look at the first item in the file folder. or examine all files for purchases over $10,000, or examine no files for sales less than $500.

Sampling error, is the incorrect selection of files for an audit.

Ex ... a random number generator tells you to audit file 1547, but you select 1457.

Sampling error is also used to describe the fact that auditing a sample will NOT create the exact same answer as auditing every single file or transaction.

What is the probability of drawing an ace or a 8?

(4 + 4) in 52, or 8 in 52, or 2 in 13, or about 0.1538.

What does is mean when the standard deviation is 0?

Intuitively, a standard deviation is a change from the expected value.


For the question you asked, this means that the change in the "results" doesn't exist, which doesn't really happen. If the standard deviation is 0, then it's impossible to perform the test! This shows that it's impossible to compute the probability with the "null" standard deviation from this form:

z = (x - µ)/σ


If σ = 0, then the probability doesn't exist.

What is the probability that this couple will have a colorblind child?

Impossible to know without information about genes that the parents have. are the parents colorblind? etc.

What is the probability of 3 tails in a row if a coin is flipped tree times?

For a fair coin it is (1/2)3 = 1/8 = 0.125

For a fair coin it is (1/2)3 = 1/8 = 0.125

For a fair coin it is (1/2)3 = 1/8 = 0.125

For a fair coin it is (1/2)3 = 1/8 = 0.125

How many ways are there to arrange the letters in ALABAMA and put four A together?


If the four letters "A" are to be together, "AAAA", then it's like having four different

letters; AAAA, L, B, M.

The number of different arrangements (permutations) of the 7 letters in the word

"ALABAMA" putting the four As together are;

4! =

4x3x2x1 =

24

What is the compound event of flipping a coin and rolling die 3 times?

define success and failure. Heads? or tails. What number or set of numbers do you want on the die? A compound event could be heads for the coin and all 3 die are less than 4.

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