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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
These are sometimes called 'electron clouds'.
How many outcomes are there from rolling 10 dice?
It depends on what you define as an outcome. Let me take a simpler case: just two dice.
1. Outcomes of possible sums of the two dice:
- 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
2. Outcomes of possible sets of two dice:
- {1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {4, 4}, {4, 5}, {4, 6}, {5, 5}, {5, 6}, {6, 6}
3. Outcomes of possible combinations of two dice:
- (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
We would need to know which you need. Assuming you want all the possible combinations of ten 6-sided dice, then it is 610, or 60,466,176.
What is the formula for calculating probability?
short answer; it depends.
Generally, you can say the probablility of an event having a specific outcome is the number of ways in which that outcome can occur divided by the total number of ways any outcome can occur. For example, the likelihood of drawing a heart from a standard 52 card deck is 13/52 because there are 13 possible results that have the desired outcome (IE 13 heart cards) and 52 total possible outcomes (52 possible cards).
On average how many people share the same birthday?
On average, in the entire world about twenty eight thousand people will have the same birthday as one another. In a room full of people, there should be two people who have the same birthday.
What is the probability of rolling a multiple of 3?
The answer depends on how often the die is rolled. As the number of rolls increases, the probability gets near enough to 1 as makes no difference.
For a single roll, the answer is 1/3.
What is the probability of drawing two red queens in a pack of playing cards?
The answer depends on how many cards are drawn, whether that is with or without replacement, whether the cards are drawn at random. If only one card is drawn, the probability is 0. If 51 cards are drawn, the probability is 1.
If two cards are drawn, at random, and the first is not replaced, the probability is
(2/52)*(1/51) = 2/2652 = 0.00075, approx.
What is the probability of getting heads at least once if a fair coin is flipped 7 times?
This is easiest calculated by calculating the probability that NO SINGLE heads is obtained; this is of course the complement of the question. The probability of this is 1/2 x 1/2 x 1/2 ... 7 times, in other words, (1/2)7. The complement, the probability that at least one head is obtained, is then of course 1 - (1/2)7, or a bit over 99%.
What are two requirements for a discrete probability distribution?
Not sure about only two requirements. I would say all of the following:
- there is a finite (or countably infinite) number of mutually exclusive outcomes possible,
- the probability of each outcome is a number between 0 and 1,
- the sum of the probabilities over all possible outcomes is 1.
The Poisson distribution, for example, is countably infinite.
What does the normal probability density function describe?
A probability density function (pdf) for a continuous random variable (RV), is a function that describes the probability that the RV random variable will fall within a range of values. The probability of the RV falling between two values is the integral of the relevant PDF.
The normal or Gaussian distribution is one of the most common distributions in probability theory. Whatever the underlying distribution of a RV, the average of a set of independent observations for that RV will by approximately Gaussian.
What are the chances of winning a prize on prize wheel?
The answer depends on the layout of the prize wheel.
Age at death.
What is the total number of possible outcomes when rolling a pair of dice work checked?
There are 36 possible outcomes.
How many different five-letter arrangements can be made from the letters in the name EULER?
There are 5!/2! = 60 arrangements.
What is the probability that if 4 letters are typed no letters are repeated?
It is (26/26)*(25/26)*(24/26)*(23/26) = 358800/459676 = 0.79 approx.
What is the probability that if 4 letters are typed with repetition allowed all 4 will be vowels?
It is (5/26)4 = 625/456,976 = 0.00137 approx.
What is the probability of rolling two number cubes simultaneously and getting different numbers?
The probability is 5/6.
What is the probability of pulling the right card from a deck of cards?
If we assume that the use of the definite article in the question implies that there is only one such card, the answer is 1/52.
If 10% of plain M&Ms are blue and you have a sample of 20 M&Ms only two of them will be blue. If you need to have 15 blue M&Ms, then your sample size should be 150 M&Ms because 15 is 10% of 150.
There are 16 possible outcomes, each of which is equally likely. So each has a probability of 1/16
HHHH: X = H*T = 4*0 = 0
HHHT: X = H*T = 3*1 = 3
HHTH: X = H*T = 3*1 = 3
HTHH: X = H*T = 3*1 = 3
THHH: X = H*T = 3*1 = 3
HHTT: X = H*T = 2*2 = 4
HTHT: X = H*T = 2*2 = 4
HTTH: X = H*T = 2*2 = 4
THHT: X = H*T = 2*2 = 4
THTH: X = H*T = 2*2 = 4
TTHH: X = H*T = 2*2 = 4
HTTT: X = H*T = 1*3 = 3
THTT: X = H*T = 1*3 = 3
TTHT: X = H*T = 1*3 = 3
TTTH: X = H*T = 1*3 = 3
TTTT: X = H*T = 0*4 = 0
So, the probability distribution function of X is
f(X = 0) = 1/16
f(X = 1) = 4/16 = 1/4
f(X = 2) = 6/16 = 3/8
f(X = 3) = 4/16 = 1/4
f(X = 4 = 1/16
and
f(X = x) = 0 for all other x
What event occurred the third?
The event after the first and second events but before the fourth, of course!
What is the coordinates for 22 s and 43 w?
22 s and 43 w are coordinates. The coordinates reference Rio de Janeiro.
