Probability

Imagine the 5 seats on the stage being filled in some order. The first seat can be occupied by any one of the 5 speakers. With each choice of 5 speakers, there are four who can go for the next seat. Then, wiyth each of the 5*4 choices, there are 3 speakers left to go for the next.

Continuing in this way, the answer is 5*4*3*2*1 = 5! = 120 ways.

In a standard deck of 52 cards, there are 13 clubs and 1 seven of hearts.

The probability of drawing a club or the seven of hearts, then, is 14 in 52, or 7 in 26.

It is 156/663 = 0.2353, approx.

The probability that the sum is seven all three times is 1/216.

The probability of flipping a heads is 1/2 and the probability of rolling a 6 is 1/6. By the laws of probability it would be logical to multiply them together, (1/2)(1/6) thus the answer being 1/12 with is roughly eight percent.

If the pack is well shuffled, the probability is 1/52.

There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes.

However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52, the probability of 3 girls out of 4 children is 0.2331

The probability is 21/26.

This is an example of an INDEPENDENT event:

The probability of throwing a double six with two dice is the result of throwing six with the first die and six with the second die. The total possibilities are, one from six outcomes for the first event and one from six outcomes for the second, Therefore (1/6) * (1/6) = 1/36th or 2.77%.

The two events are independent, since whatever happens to the first die cannot affect the throw of the second, the probabilities are therefore multiplied, and remain 1/36th.

The sum of a set of data divided by the number of pieces of data is the average or mean.

A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance.

A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.

11/18 x 10/17 = .359

If you roll a pair of six sided number cubes the probability of rolling two numbers whose sum is 6 is 5/36 or 0.1389. There are 5 ways to get 6: 1,5 & 5,1 & 4,2 & 2,4 & 3,3. There are 36 outcomes for a roll of 2 dice.

Probability of Jack being drawn is 4/52 since there are 4 Jacks and 52 cards in the deck. Also, the probability of drawing a Queen and King is 4/52. So, if you draw one card from a normal deck of cards the probability of drawing a jack or queen or king is 4/52 + 4/52 + 4/52 = 12/52 or 3/13 or 0.2308.

For standard dice, there are 36 outcomes for rolling 2 dice. There are 3 ways to roll a 4; 3,1 1,3 & 2,2. The probability of sum of 4 is then 3/36 or 1/12 or 0.0833.

Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.

Separate them by colour

Given any sample size there are many samples of that size that can be drawn from the population. In the population is N and the sample size in n, then there are NCn, but remember that the population can be infinite.

A test statistic is a value that is calculated from only the observations in a sample (no unknown parameters are estimated). The value of the test statistic will change from sample to sample. The sampling distribution of a test statistic is the probability distribution function for all the values that the test statistic can take across all possible samples.

The two dice sum of 4:

1,3

2,2

3,1

= 3 in 36

= 1 in 12

2, one jack of diamonds one jack of hearts.

The z-score is 0.84. In the related link, look in the body of the table for .3 area (.2995 closest) and it yields the .84 z-score.

5 letters in first position there can be any one of the five, in the second position there are four possibilities left, in third position one of three remaining letters etc. 5 * 4 * 3 * 2 *1 = 120.

3 out of 8

Percentage