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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
Is uniform distribution bimodal?
The modes of a probability density function might be defined as the (countable) set of points in the domain of the function for which the function achieves local maxima. Since the probability density function for the uniform distribution is constant by definition it has no local maxima, hence no modes. Hence, it cannot be bimodal.
What is the probability of choosing a queen or a king from standard deck of 52 playing cards?
The answer depends on how many cards are drawn, whether or not at random, with or without replacement. The probability for a single card, drawn at random, from a normal deck of playing cards is 2/13.
The answer depends on how many cards are drawn, whether or not at random, with or without replacement. The probability for a single card, drawn at random, from a normal deck of playing cards is 2/13.
The answer depends on how many cards are drawn, whether or not at random, with or without replacement. The probability for a single card, drawn at random, from a normal deck of playing cards is 2/13.
The answer depends on how many cards are drawn, whether or not at random, with or without replacement. The probability for a single card, drawn at random, from a normal deck of playing cards is 2/13.
from itertools import permutations
from string import join
arrangements = [ ]
for p in permutations ( 'ugccsir', 6 ) :
arrangement = join ( p, '' )
if 'ui' in arrangement :
continue
if not arrangement in arrangements :
arrangements . append ( arrangement )
print len ( arrangements )
The above Python code gives a result of 2,220.
What is the probability that 13 rolls of a fair die will show three threes?
Not an easy question. Here's a long but logical answer.
The chance of not getting a 3 on any throw is 5/6, so the chance of not getting any threes in the first 10 throws is (5/6)^10.
Now, having reached that point, the chance of throwing three threes in the last three throws is 1/6 x 1/6 x1/6 or 1/216. So the probability of throwing three threes in any chosen three throws is (5/6)^10 x 1/216. This should seem logical because the probability of throwing three threes in the first three throws followed by ten failures to throw threes, should be the same as just getting threes in the last three throws. The probability is the same for getting threes in only the second, fourth and sixth throw, or any other combination of three throws.
Now, there are a set number of combinations of 13 things taken in groups of three. This is given by the formula for C(13,3) =
(13x12x11x10x9x8x7x6x5x4)/((10x9x8x7x6x5x4x3x2x1)x(3x2x1)). That cancels down to (13x12x11)/(3x2x1), and equals 286.
So, there are this many ways you can pick out three throws which you want to be the threes, and the probability of them actually being threes is the first calculation we did.
The answer to the question is 286 x (5/6)^10 x 1/216 which is 0.2138453, about.
The inequality with the terms 2x, 3 and 7 can be written as 2x -3 = 7, 2x + 3 = 7, 2x * 3 = 7, and 2x/3 = 7. This means that the solutions are 5, 2, 7/4, and 21/2 respectively.
Why is a two-tailed test preferred over a one-tailed test?
In general, it is not. A one-tailed test is more powerful but it does require the alternative hypothesis to be one sided and, in therefore requires some expectation about the observations if the null hypothesis is not true.
The question, therefore, is appropriate only when the experimenter has extremely limited information about the experiment - not a very common occurrence.
In general, it is not. A one-tailed test is more powerful but it does require the alternative hypothesis to be one sided and, in therefore requires some expectation about the observations if the null hypothesis is not true.
The question, therefore, is appropriate only when the experimenter has extremely limited information about the experiment - not a very common occurrence.
In general, it is not. A one-tailed test is more powerful but it does require the alternative hypothesis to be one sided and, in therefore requires some expectation about the observations if the null hypothesis is not true.
The question, therefore, is appropriate only when the experimenter has extremely limited information about the experiment - not a very common occurrence.
In general, it is not. A one-tailed test is more powerful but it does require the alternative hypothesis to be one sided and, in therefore requires some expectation about the observations if the null hypothesis is not true.
The question, therefore, is appropriate only when the experimenter has extremely limited information about the experiment - not a very common occurrence.
What is the probability of numbers 5 and above?
The answer depends on what the experiment is and since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
The answer depends on what the experiment is and since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
The answer depends on what the experiment is and since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
The answer depends on what the experiment is and since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.
What are the properties of a standard normal curve?
It is a normal curve with mean = 0 and variance = 1.
What is the probability of rolling a number divisible by 3 with two rolls of a fair number cube?
The probability of rolling a number divisible by three on a fair die (3 and 6) is 2 in 6, or 1 in 3, or about 0.3333. Since there are 36 permutations of rolling two dice, the probability, then, of rolling (at least one) number divisible by three on two rolls of a die is 19 in 36, or about 0.5278. Simply count the number of desired results, and divide by the number of possible results, as I have done below.
11
12
13 x
14
15
16 x
21
22
23 x
24
25
26 x
31 x
32 x
33 x
34 x
35 x
36 x
41
42
43 x
44
45
46 x
51
52
53 x
54
55
56 x
61 x
62 x
63 x
64 x
65 x
66 x
If, on the other hand, you are looking at the probability of rolling a sum divisible by three, consider ...
11 2
12 3 x
13 4
14 5
15 6 x
16 7
21 3 x
22 4
23 5
24 6 x
25 7
26 8
31 4
32 5
33 6 x
34 7
35 8
36 9 x
41 5
42 6 x
43 7
44 8
45 9 x
46 10
51 6 x
52 7
53 8
54 9 x
55 10
56 11
61 7
62 8
63 9 x
64 10
65 11
66 12 x
... which is 12 in 36, or 1 in 3, or about 0.3333.
Is the higher the standard deviation the greater the variation?
Yes. Since the standard deviation is defined as the square root of the variance, it can be said that the higher the standard deviation, the higher the variance.
What does standard deviation value indicate?
The standard deviation for a set of data is a measure of how much the individual observations are spread about their mean. A small value indicates that they are all tightly packed around the mean value whereas a large value indicates that the observations are not so close together.
What is symmetrical normal distribution?
The Normal distribution is, by definition, symmetric. There is no other kind of Normal distribution, so the adjective is not used.
When rolling two dice what are the odds of rolling both even numbers?
The probability of rolling two even numbers on two standard dice is 0.52, or 0.25.
What is the probability of drawing a red 4 from a deck of cards?
There are two red fours in a standard deck of 52 cards, the Four of Hearts, and the Four of Diamonds. The probability, then, of drawing one of them is 2 in 52, or 1 in 26, or about 0.0385.
How do you calculate a raw score from a z score?
z = (x - μ) / σ is the formula where x is the raw score and z is the z-score. μ and σ are the mean and standard deviations and must be known numbers.
Multiply both sides by σ
zσ = x-μ
Add μ to both sides
μ + zσ = x
x = μ + zσ
You calculate the raw score x , given the z-score, μ and σ by using the above formula.
What is the probability of getting tails on the first toss and heads on the second toss?
1 in 2 to get tails on first toss
1 in 2 to get heads on second toss
To get tails on first toss and heads on second toss, probability is
1/2 x 1/2 = 1 in 4
As there are 4 queens in a 52 cards deck the probability is P=4/52=1/13
If I understand the question correctly, the answer is 1/120.
What are odds of being murdered in lifetime?
1 in 33.8
The current world homicide rate is 7.6 murders per 100,000 people which translates to a .0076% chance per year. Assuming a 100 year lifespan that would theoretically mean a .76% chance of getting murdered in your lifetime, but that is totally off from the true value because likelihood changes based on many factors, the most basic of which include location and age. I don't know where the person who wrote 1 in 33.8 (2.96%) got that statistic but by my math that is an extreme overestimate unless you live in southern Africa or central America.
What is the z-score for the area equals 0.7704?
In a standard normal distribution curve, one half of the area is .5 (or 50%). 0 is the middle value of the z-score. So, for an area of .7704, z must be negative. Also, the area from 0 to z (which is negative) must be equal to .2704. From the normal probability table, this value is -0.74
Therefore, the z-score for the area equals 0.7704 is -0.74
How many standard deviation tend to cover the entire range of scores in a distribution?
Type your answer here...
It depends what percentage of the total data you want to embrace. 99.73% of the total distribution lies between minus to plus 3 standard deviations. That's usually the benchmark range.
How many different ways can you arrange 5 out of 7 books on a book shelf?
There are only 5 places on the shelf. You have 7 books to choose from. We will ignore the order of the books on the shelf. The first place can be filled from a choice of 7 books, the next place from 6, the next place from 5, the next from 4, and the last of the 5 places from 3 books.
So the number of ways of choosing the 5 is found from 7 * 6 * 5 * 4 * 3 = 2520
How many permutations are in the word mathematics?
The word MATHEMATICS has 11 letters. The number of permutations of 11 things taken 11 at a time is 11 factorial (11!), or 39,916,800.
What is the probability of picking a prime number from numbers between 1 and 20?
The probability is 8/20.
