Probability

If you mean like a coin toss, it's 50% probability of winning, also known as even or 1:1 odds.

Winning once has a probability of p=0.5. Winning twice has a probability of p*p = p^2 = 0.25 = 25% = 1/4 = "1 chance in 4" = "odds of 3 to 1 against."

Sampling bias.

The probability of drawing a queen or a four from a standard 52 card deck is 8 in 52, or 2 in 13, or about 0.1538.

Probabilities go from 0 to 1. 1 means the event will definitely happen. 0 means it's impossible for it to happen. 0.5 means it's just as likely to happen as not. Once you are aware of this scale, it is clear that an event with probability 0.95 is more likely to happen than an event with probability 0.10.

(assuming that the probability of having a girl or a boy is 50/50)

Looking from beforehand, the probability of having three boys then a girl is the probability of each of these events happening multiplied together. That is 50% x 50% x 50% x 50% or 0.54 This would mean that the chance of having a girl after three boys is 0.0625.

If you've already had the three boys though, it is a different story. The point is that previous experiences do not affect future ones; probability has no memory. Thus the probability of having a girl next is 50%, regardless of if you've had boys or girls in the past. To think otherwise is known as the gambler's fallacy, where a gambler says "black has come up 4 times in a row, it must be red next" even though the chance of red is always 50%

They are b, l, p, r, t and y (although the y acts as a vowel).

A fully extended standard windsock, per FAA standards, means the wind is at least 15 knots or 17 MPH.

Possible results when rolling the first cube = 6

Possible results when rolling the second cube = 6

Possible results when rolling two cubes = 6 x 6 = 36

How many of these 36 possibilities are snake-eyes ? Only 1 .

Probability of snake-eyes on the first roll = 1/36

Probability of snake-eyes on the second roll = 1/36

Probability of snake-eyes on both rolls = 1/36 x 1/36 = 1/1,296 = 0.077 percent

Odds = (1 in 1,296) or (1,295 to 1) against it.

The probability of failure.

Actually, the phrases used have very confusing connotations. When studying the risk of people being killed by lightning strikes, a "success" or the "desired outcome" is death caused by lightning. I somehow doubt that the person struck would consider it a desired outcome or a success!

Probability is the likelihood, expressed in numerical or ratiometric terms, that an event will occur. A probability of 1 means that the event will occur. A probability of 0 means that the event will not occur. A probability of 0.5 means that the likelihood of the event occurring is equal to the likelihood of it not occurring. For instance, a fair coin has a 0.5 probability of being heads, and a 0.5 probability of being tails.

Defined formally, probability is the number of permutations of the desired outcome divided by the number of permutations of all possible outcomes. Take a standard six-sided die, for instance. There are six permutations. One of them is a 1, so the probability of rolling a 1 is 1 in 6, or about 0.1667.

Probability is not assured. If you roll a die 600 times, you will not necessarily get 100 1's. Over the long run, you will approach that outcome, but each trial will have different results. This is the difference between theoretical probability and experimental probability - theoretical being the mathematical estimate - experimental being the observed results.

The probability of drawing a diamond from a standard 52-card poker deck without jokers is 13/52, or 1/4.

The probability of drawing a second diamond at that point would then be 12/51, for an overall probability of 12/212, or 3/53. This amounts to about a 5.88% chance.

It is approx 0.44

1/2 or 5/10

Standard deviation is the square root of the sum of the squares of the deviations of each item from the mean, i.e. the square root of the variance. In order to increase the standard deviation, therefore, you need to increase the average deviation from the mean.

There are many ways to do this. One is to move each item further away from the mean. For example, take the set [2, 4, 4, 4, 5, 5, 7, 9]. It has a mean of 5 and a standard deviation of 2.14. Multiply each item by 2.2 and subtract 5, giving the set [-1.3, 2.9, 2.9, 2.9, 5, 5, 9.2, 13.4], effectively moving each item 10% further away from the mean. This still has a mean of 5, but the standard deviation is 4.49.

A higher standard deviation means that the data are fluctuating more widely with respect to the mean. It could mean there are some bad samples, or it could simply mean that the data are not as tightly bound to the mean as anticipated. An unexpected standard deviation should be evaluated, using more robust analyses techniques, so as to differentiate between the various explanations. This is an expected part of error analysis, without which an analysis is incomplete.

9

Because the whole population might be too large to sample.

A good example is the population of the world. At nearly 7 billion people, it would be unrealistic to sample each person to determine some factor that you are looking at. Generally, we sample a subset of the population, taking into account differences (or errors) that might result, in this case, regional and cultural, in order to estimate the behavior of the larger population.

5 to 1 to win means the probability of actually winning is 1 to 5, or 0.2. The larger the payout, the longer (or poorer) the odds.

Actually, 5 to 1 means 1 chance in 6 or 16.7%. Of course, race track odds may not be the true probablity of winning.

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 probability is 1. The letters in the word mathematics are all constants, not variables!

Probability; Possibility/ Likeliness of an outcome

A dichotomous trial is one for which there are only two possible outcomes. Another name for it is binary outcome.

(1 in 52) or about 0.01923.

It is approx 0.001824