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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
If it lands on a six 140 times then the estimated probability of a six is 140/400 = 0.35
What is the probability the number contains at least one digit 2?
The probability is 1. And the same is true for any other digit.
This counter-intuitive result can be proved as follows:
Ignore numbers with leading zeros.
There are 9 1-digit numbers of which 8 do not contain any 2s;
There are 90 2-digit numbers of which 8*9 do not contain any 2s;
There are 900 3-digit numbers of which 8*9*9 do not contain any 2s;
and so on.
The total number of k digit numbers is 9 + 90 + 900 + ... + 9*10^(k-1)
= 9*[10^k-1]/[10 - 1] = 10^k - 1
Of these, the count of numbers which do not contain any 2s = 8 + 8*9 + 8*9^2 + ... + 8*9^(k-1)
= 8*[9^k-1]/[9 - 1] = 9^k - 1
So the probability that the numbers do not contain any 2s is [9^k - 1]/[10^k - 1] which, as k gets larger, approaches 9^k/10^k = (0.9)^k which tends to 0.
So, the probability that the number DOES contain at least one 2 = 1 - Pr(It contains none) = 1 - 0 = 1.
Why you prefer Normal Distribution over the other distributions in Statistics?
For theoretical reasons (such as the central limit theorem), any variable that is the sum of a large number of independent factors is likely to be normally distributed. For this reason, the normal distribution is used throughout statistics, natural science, and social science as a simple model for complex phenomena.
Sir names 1st Senior second Junior third the third when is it ever the second?
I am a 2nd and not a junior. I have the same name as my Grandfather. If I were to have the same name as my father I would be a junior. If I give my son the same as myself he would be a junior and a 3rd.
What is the chance of being shot by a random gunman?
Pretty slim in the US or most of Europe and Asia. If you are in Africa or the Middle East you would have a significantly higher risk. Still relatively small though, you're much more likely to die in a car acccident than from a random gunman.
The probability of observing a z value equal to or more extreme than 1.50 is 0.1336
What is the probability of drawing a king or a 9 from a standard 52 card deck of cards?
The probability of drawing a king or a nine from a standard deck of 52 cards is (4 + 4) in 52, or 8 in 52, or 2 in 13, or about 0.1538.
Your risk of getting pregnant is the same as any other time when you are fertile. Unless you are menopausal or pregnant, you have a chance of becoming pregnant from having sex.
What is the probability of rolling a 5 or 6 on a die?
1 out of six for both five and six well that's for the original die wich is 1 of each number from 1 to 6 it depends how many sides it has
What is the probability of drawing a red number card from a deck of cards?
13 out of 52.
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It should be 20 out of 52 if Ace is included as a number card.
Not including ace the probability is 18 out of 52.
What is the probability of drawing 2 aces from a 52 card deck?
Let A= getting an ace the first time
and B= getting an ace the second
We are looking to for the probaliity of getting A and B that is P(A and B)
We know P(A and B) = P(A) . P(B|A)
= (4/52) . (3/51) = 1/122 = .00452
NOTE that P(B|A) is the conditional probability of getting an ace the second time given that you got an ace the first time.
Why are random samples more representative of the population than other kinds of samples?
A 'random' sample - covers all age groups, genders, and other criteria. A 'targeted' sample might only cover a small part of the population.
The answer is 4! (4 factorial), the same as 4x3x2x1, which equals 24 combinations.
The answer is 24 and this is how:
A b c d
A b d c
A c d b
A c b d
A d c b
A d b c
B c d a
B c a d
B d a c
B d c a
B a c d
B a d c
C d a b
C d b a
C a b d
C a d b
C b d a
C b a d
D a b c
D a c b
D b c a
D b a c
D c a b
D c b a
What is the probability of winning a reverse raffle with 200 numbers?
for each ticket, it is the same as a regular raffle: one in 200
What is one standard deviation above the mean 700?
The mean alone is not enough to provide an answer.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
What is the probability of picking 2 aces from a standard deck?
(4 in 52) times (3 in 51) or (12 in 2652) or (1 in 221) or about 0.004525.
