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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 is a z score and what its used for?

The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities.

However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference.

The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.

What are all possible outcomes of 124?

As long as the 124 just sits there without having anything done to it, there are no outcomes.

Can you take of cards has 52 cards in the deck can be divided into four parts of exactly 13 card each describe all the other ways to death can be divided into equal piles?

It can be divided into even piles of:

  • 52 piles of 1 card each.
  • 26 piles of 2 cards each
  • 13 piles of 4 cards each
  • 4 piles of 13 cards each
  • 2 piles of 26 cards each
  • 1 pile of 52 cards.

What are the patterns if three coins are tossed?

They are:HHH,

HHT, HTH, THH,

HTT, THT, TTH,

TTT.

What is the chance the 2 cards drawn from a stack of cards numbered 1 through 10 will have a sum of 9?

There are two possible results:

If there are only 10 cards in the stack

Out of the possible outcomes of drawing two cards, 4 outcomes have a sum of 9.(1+8, 2+7, 3+6, 4+5)

The total number of potential combinations are 10 potential choices for the first card and 9 for the second or 10x9=90

The odds of drawing the desired total (9) is 4/90 or 1 in 22.5

If there are more than 10 cards in the pile (several runs of 1-->10).

There are still a limited number of 2 card combinations that sum to 9:

1+8, 2+7, 3+6, 4+5

The number of combinations of cards that can be drawn are 10 potential choices for the first card and 10 for the second or 10x10=100.

The odds of drawing the desired total (9) is 4/100 or 1 in 25

How many possible outcomes if a coin is tossed 4 times?

2^2^2^2

* * * * *

Actually, the conventional notation is

either 2*2*2*2 or 2^4 = 16

What are the chances of rolling an odd number on a die?

Total possible outcomes of a single roll of a single die (1, 2, 3, 4, 5, 6) = 6

Odd numbers (1, 3, 5) = 3

Probability of an odd number = 3/6 = 1/2 = 50%.

If a six sided dice is thrown What is the probability that the score is a five?

You said "a" six sided dice. Though the singular is "die".

If you mean one die, the odds are 1 in 6 of it turning up five, or about 16.6%.

If you meant two dice, the odds are four out of thirty six, or 1/9th, or about 11%.

What are the characteristics of continuous distribution?

The probability distribution function (pdf) is defined over a domain which contains at least one interval in which the pdf is positive for all values.

Usually the domain is either the whole of the real numbers or the positive real numbers, but it can be a finite interval: for example, the uniform continuous distribution.

Also, trivially,

the pdf is always non-negative,

the integral of the pdf, over the whole real line, equals 1.

Which equation implies that A and B are independent events?

A and B are independent events if the probability of their intersection equals the product of their individual probabilities, which is mathematically expressed as P(A ∩ B) = P(A) * P(B). This means that the occurrence of event A does not affect the occurrence of event B and vice versa. If this equation holds true, then A and B can be considered independent.

What is the probability of not getting a 7 or 11 on either of two tosses of a pair of dice?

First we find the probability of getting a 7. Of the 36 outcomes possible 6 result in a sum of 7, in other words 1/6. The probability of getting an 11 is 2/36 or 1/18. The probability of getting one or the other is the sum of the two, 8/36 or 2/9. The proability of getting neither is equal to the probability of getting anything other than 7 or 8. We find this value by subtracting 2/9 from 1. So the probability of not getting 7 or 11 is 7/9.

Will it be raining Monday?

Very definitely, YES. It will be raining - somewhere on earth at any given moment of time.

What is the probability that a family with four children has all boys given that the first two are boys?

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 the other two being boys is 0.2672.

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