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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 experimental probability of correctly guessing at exactly zero correct answers?
I regret that I do not have access to a study that looked at this matter and so do not have any experimental evidence.
Which conditions must be met to conduct a test for the difference in two sample means?
The two samples must be independent and the data must be at least ordinal. Under those conditions the Mann-Whitney U test can be used.
What is the probability that Alex makes both of his shots?
The answer depends on the probability that Alex makes a single shot.
How many different ways can you arrange 5 letters in a row?
5 choices for the first, 4 for the second .... so is 5x4x3x2x1 = 120 ways. If 2 of the letters are the same then for any arrangement, switching those 2 doesn't make any difference, so divide the answer by 2. If 3 are the same then there are 3x2x1 ways of shuffling those, which at first were all different arrangements but now are not, so divide by 3x2x1 ie 6.
Is homogeneous uniform distribution?
Your question cannot be answered as stated. Please explain further.
Given the way you have worded the question I take it to mean, what is the probability of drawing at least one spade?
We can do this most easily by asking first, what is the probability of drawing no spades on each of the 80 times. This is 39/52. The probability of doing this 80 times is (39/52)80.
Then the probability of not doing this is 1 - (39/52)80, which is quite close to one. The probability of drawing at least one spade is almost one.
What is the probability of an impossible event if zero is empirical?
The probabilit of an impossible event is 0. Empiricism has nothing whatsoever to do with it.
What is the probability of observing exactly one 3 when rolling a fair die five times?
Same as for rolling 5 dice at the same time, namely 5 x 1/6 x (5/6)4 This is the second last term in the expansion of (a + b)5 where a is the probability of a die falling at 3 (ie 1/6) and b is the probability of it not falling at 3 (ie 5/6) and the various terms of the expansion correspond to the various combinations : a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5. Which of course adds up to 1 when you allow all possibilities, not just one 3.
Never!
What is the probability of guessing a 7 and getting it correct?
It depends on what the questionis and what you can choose from.
What does events are mutually exclusive mean?
Two events are mutually exclusive if the occurrence of one event implies that the other cannot occur. There is no need for either to occur.
For example, if you roll a die and the two outcomes of interest are:
A - you roll a prime
B - you roll a composite
then A and B cannot occur together. Of course, you could roll a 1, so that neither A nor B occurs.
An example of events that are not mutually exclusive is:
A - you roll a prime
C - you roll an even number
If you roll a 2 then both A and C occur.
What is the probability of rolling a number less than a 6 on a set of dice?
The answer depends on how many dice are in the SET of dice.
This question cannot be answered for two reasons.
- The questions states that "... the probability of each failing [is] 2 ...". That is not possible since probabilities can never be greater than 1.
- The question does not specify what even the probability is required for: the guidance system failing or not failing!
Is the number of all possible outcomes of an experiment. The number depends on the experiment.
What is the highest card number in standard deck of cards?
The highest number card in a standard deck of cards is the number ten. Some games use the picture cards to represent values higher than ten but there are no numbers on these cards.
What does four twos in a row stand for?
Four twos in a row is a term used in probability. It is also used in card games. It means that the player has dropped two suits of twos consecutively.
What is the probability of getting 3 sixes in 5 tosses of a die?
125/3888 or 3.22%.
A shortcut can be taken instead of the traditional tree-method or combination counting:
Assume that there are 5 "spots" in which the 3 sixes can be placed. Using the nCr probability formula, we find that there are 10 different arrangements of 3 sixes in 5 spots. (5!/((5-3)!*3!)). This simplifies to (5*4)/2, which is 10.
A visual of this:
6-6-6-X-X
6-6-X-6-X
6-6-X-X-6
6-X-6-6-X
6-X-6-X-6
6-X-X-6-6
X-6-6-6-X
X-6-6-X-6
X-6-X-6-6
X-X-6-6-6
Next, all we need to do is figure out how many different combinations of each of the above combinations there are. Since there are only two variable numbers (denoted X) in each combination, and each can only be an integer from 1-5, we can determine that for each combination above there are 25 subsequent combinations (5^2).
Finally, (10*25)/(6^5) = 125/3888.
What does probability level mean?
The probability level for an outcome is the probability that the outcome was at least as extreme as the one that was observed.
How can the probability of a Type 1 error be reducued?
- In some cases a choice of tests may be available; some tests are more powerful than others.
- Use a larger sample.
- There is a trade-off between Type I and Type II errors so you can always reduce the Type I error by allowing the Type II error to increase.
Where can someone play Bubble Spinner?
One can play the game Bubble Spinner online for free from the Bubble Spinner website. It is also available from Addicting Games. Bubble Spinner is a puzzle game where one shoots rotating bubbles from a fixed target.
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.
