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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 probability explain in detail?
Probability is the likelyhood that some particular outcome will occur. It is expressed as a number between 0 and 1, with 0 meaning there is no likelyhood at all, and with 1 meaning it is guaranteed to happen.
A simple example is the flipping of a coin. There is a 0.5 probability of getting heads, and there is a 0.5 probability of getting tails. Assuming a fair coin.
Another example is a standard deck of 52 playing cards. There is a 0.25 probability of getting a Heart, and there is a 0.75 probability of not getting a Heart.
Probability is not an exact predictor of outcome. If you flipped a coin 100 times, for instance, you would expect about 50 of the throws to be heads, but you will not get that exact outcome. Even if you throw the coin 10 million times, you will not get exactly 5 million heads. What happens is that, as the number of trials increases, the closer the experimental results are to the theoretical probability.
One important factor of probability is that the sum of the probabilities of all possible outcomes is equal to the number of all possible trials. Stated another way, the sum of all probabilities is always equal to exactly 1. Stated yet another way, the probability that something is going to happen is 1.
This can get complicated, particularly when the number of outcomes is large. Take the New York State lottery game Lotto, for instance - you pick 6 numbers out of 59 - there are so many popssible results that special mathematics (the science of permutations and combinations) is used to do that calculation. In this case, there are 45,057,474 combinations of 59 things taken 6 at a time, so the odds of winning the jackpot on one game is 1 is 45,057,474 or about a probability of 0.00000002194. Another way to say this is that the probability of not winning the jackpot is about 0.9999999778.
I have only scratched the surface on this topic. Any other contributor is, as always, welcome to refine this answer.
What is the probability of rolling a number other than 3?
There are 6 sides of a die, and rolling a 3 is one of the 6 sides.
Therefore, there are 5 sides on the die which is not a 3.
So, (outcomes wanted)/(total outcomes) = 5/6
Why are standard z values so important?
A z-score gives the distance (specifically number of standard deviations) from the mean so when you compare z-scores, it gives a direct comparison of how far from the mean the values are.
What is the probabilty of getting a heart from a ordinary pack of cards?
There are 52 cards in a deck with no jokers. There are 13 hearts in such a deck so the probability of drawing a heart is
13/52
Within 1 stdev of the mean - between 40 and 60.
What is the probability of drawing a 3 out of a deck of cards?
There are four 3 cards in the deck of 52 cards. So the probability of drawing a 3
from the deck of cards is; P(3) =
4/52 =0.076923076... ~ 0.0769 ~ 7.69%.
What is the probability of rolling a 3 when a number cube is rolled twice?
If you mean rolling at least one three, the 1/3.
If you mean exactly one three, then 5/18.
and
If you mean a sum of 3 for the two throws, the answer is 1/18
What does the mean have to do with a normal distribution?
Almost all statistical distribution have a mean. It is the expected value of the random variable which is distributed according to that function.
Is it true that the past outcomes of coins flips greatly affect the outcomes of furture coin flips?
It's human nature to think so, but no. Even after getting 100 heads in a row, the odds of the next flip being heads is still 50%.
On a random draw of a single card, it is 16/52 = 4/13.
The odds of a woman having twins on new years even where on baby is born in the final minutes of the year and the other born in the beginning minutes of the next year is considered a rarity and only a handful of cases are reported each year.
What is the probability of drawing a red card and a 7 in a deck of cards?
The probability of doing so, if the first card is not replaced, is 0.0385, approx.
It is 10/52 = 5/26.
From a well shuffled and complete deck without the Jokers, pulling one card and getting a heart or spade is one in two. Getting a spade is a one in four shot. (Four suits, equal number of cards in each suit....) Same for club, heart or diamond. Getting a spade or a heart is a one in four plus a one in four or one in two. It's fifty-fifty. The probability of drawing a heart or a spade when 1 card is picked up from a well shuffled (complete) deck (without Jokers) is 0.5 or one half.
Two out of nine. 2:9.
an optimistic one
The odds of getting 4 cards in any particular suit (for example, hearts) would be:
1/4*1/4*1/4*1/4=1/256.
The odds of getting 4 cards of the same suit (any suit) would be 4x greater:
1/256*4=1/64
Because it doesn't matter what the last card is, the probability is 1/64.
How many people are up right now?
If you consider that there on about 6 billion (6,000,000,000) people, give or take, on the Earth, and you assume an average sleep time of 8 hours, then two thirds of the population are up at any one time. This is about 4 billion people.
What is the probability of drawing a Club or a Queen of Spades from a deck of 52 cards?
P(club) + P(QS) 1/4 + 1/52 = .25 + .0192 = .269
yss
True.
What is the probability of rolling a six sided die 20 times and getting a 5?
Suppose A is the event {rolling a 6-sided die 20 times and getting a 5}
Then A', the complement of A, is the event {rolling a 6-sided die 20 times and not getting a 5 any times}
So Pr(A) = 1 - Pr(A') = 1 - (5/6)20 = 1 - 0.026084 = 0.973916 (to 6 dp)
What is the probability of pulling 7 spades in a row from a deck of 52 cards?
The answer is 8,648,640 in 674,274,182,400 or approximately 0.128%.
To pull seven spades in a row from a deck of 52 cards may be translated as follows:
In a deck of 52 cards there are 13 spades, so 13 chances to pull a spade or 13/52.
After pulling one spade, there are 12 spades left and 51 cards left, so 12 chances to pull a spade or 12 / 51.
After pulling the second spade, there are 11 spades left and 50 cards left, so 11 chances to pull a spade or 11 / 50.
Continuing the above logic to the natural conclusion, we get the following multipliers:
13 / 52 * 12 / 51 * 11 / 50 * 10 / 49 * 9 / 48 * 8 / 47 * 7 / 46
which is equal to 8,648,640 / 674,274,182,400 or approximately 0.128%.
The probability of rolling 4 and 4 on a single roll of two dice is 1 in 36. You don't have to count. The probability of rolling 4 on one die is 1 in 6. The probability of rolling two 4's is (1 in 6) squared or 1 in 36. If you insist on counting, go ahead, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, etc. You will find 36 combinations, with only one 44 in them, hence 1 in 36.
