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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
When rolling two dice what are the odds of not rolling a 1 or 2 25 times in a row?
The odds of not rolling a 1 or 2 with two dice is 35 in 36. The odds of doing that 25 times in a row is (35/36)25 or about 0.4945
Note: The odds of not rolling a 1 is zero, so the answer degraded to the odds of not rolling a 2.
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Opinion #2:
-- There are 36 possible outcomes when 2 dice are rolled.
-- Only one of the outcomes is a 2.
-- So the probability of NOT rolling a 2 with 2 dice is 35/36 .
-- In 25 consecutive rolls, the probability of never rolling a 2 is (35/36)25 = 49.45% .
-- The 'odds' are 1,011 to 989 against it.
The probability of getting 3 aces in the order AAABB
is; P(AAABB)
=
(4/52)∙(3/51)∙(2/50)∙(48/49)∙(47/48) =
0.0001736...
There are 5C3 =
5!/(3!∙(5-3)!) =
10 different ways in which the aces can come
out.
So the probability of getting exactly three aces in a five card poker hand dealt
from a 52 card deck is, P(3A)
~ 10∙(0.0001736) ~ 0.001736 ~ 0.1736%
How do you calculate standard normal variate?
You use the z-transformation.
For any variable X, with mean m and standard error s,
Z = (X - m)/s is distributed as N(0, 1).
You use the z-transformation.
For any variable X, with mean m and standard error s,
Z = (X - m)/s is distributed as N(0, 1).
You use the z-transformation.
For any variable X, with mean m and standard error s,
Z = (X - m)/s is distributed as N(0, 1).
You use the z-transformation.
For any variable X, with mean m and standard error s,
Z = (X - m)/s is distributed as N(0, 1).
D+J = 328
M+D = 176
J = 5M
D+5M = 328
D+M = 176 subtract
4M = 152
M = 38
D = 176-38 = 138
What would -2 standard deviation below the mean be?
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
It would mean that the result was 2 standard deviations above the mean. Depending on the distribution of the variable, it may be possible to attach a probability to this, or more extreme, observations.
For a die it is 1/3. For anything else (a spinner, for example), there is not enough information.
For a die it is 1/3. For anything else (a spinner, for example), there is not enough information.
For a die it is 1/3. For anything else (a spinner, for example), there is not enough information.
For a die it is 1/3. For anything else (a spinner, for example), there is not enough information.
There are 100 ways - including those where one participant wins both prizes.
There are 100 ways - including those where one participant wins both prizes.
There are 100 ways - including those where one participant wins both prizes.
There are 100 ways - including those where one participant wins both prizes.
What does it mean to find the compliment of the probability of an event?
The complement (not compliment) of the probability of event A is 1 minus the probability of A: that is, it is the probability of A not happening or "not-A" happening.
The complement (not compliment) of the probability of event A is 1 minus the probability of A: that is, it is the probability of A not happening or "not-A" happening.
The complement (not compliment) of the probability of event A is 1 minus the probability of A: that is, it is the probability of A not happening or "not-A" happening.
The complement (not compliment) of the probability of event A is 1 minus the probability of A: that is, it is the probability of A not happening or "not-A" happening.
What is theoretical probability and theoretical probability?
They are the same. They are probabilities that are calculated from some theoretical model of the experiment using scientific laws.
They are the same. They are probabilities that are calculated from some theoretical model of the experiment using scientific laws.
They are the same. They are probabilities that are calculated from some theoretical model of the experiment using scientific laws.
They are the same. They are probabilities that are calculated from some theoretical model of the experiment using scientific laws.
What is the probability of 3 tails in a row if a coin is flipped tree times?
For a fair coin it is (1/2)3 = 1/8 = 0.125
For a fair coin it is (1/2)3 = 1/8 = 0.125
For a fair coin it is (1/2)3 = 1/8 = 0.125
For a fair coin it is (1/2)3 = 1/8 = 0.125
How many ways are there to arrange the letters in ALABAMA and put four A together?
If the four letters "A" are to be together, "AAAA", then it's like having four different
letters; AAAA, L, B, M.
The number of different arrangements (permutations) of the 7 letters in the word
"ALABAMA" putting the four As together are;
4! =
4x3x2x1 =
24
What is the compound event of flipping a coin and rolling die 3 times?
define success and failure. Heads? or tails. What number or set of numbers do you want on the die? A compound event could be heads for the coin and all 3 die are less than 4.
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 does a probability tree look like?
A tree on its side, with the trunk on the left and an increasing number of branches to the right.
A tree on its side, with the trunk on the left and an increasing number of branches to the right.
A tree on its side, with the trunk on the left and an increasing number of branches to the right.
A tree on its side, with the trunk on the left and an increasing number of branches to the right.
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.
How many possible outcomes are their when you roll five six sided dice?
Here are two ways you can solve this, depending on if order matters or order does not matter:
Order of the dice does matter:
Assuming that you roll a 1, 1, 1, 1, 4 is not the same as rolling a 1, 4, 1, 1, 1
Think of 5 blanks first (one for each six sided dice).[ dice 1 ] [ dice 2 ] [ dice 3 ] [ dice 4 ] [ dice 5 ]
Each dice has 6 sides, so you can have 6 different possibilities per dice. Fill in each blank with how manypossibilities. Then multiply them.
(6) x (6) x (6) x (6) x (6) = 65 = 7776 possibilities.
A few possibilities looks like (I'm not listing all 7776possibilities):
(1, 1, 1, 1, 1), (2, 1, 1, 1, 1), (3, 1, 1, 1, 1), (4, 1, 1, 1, 1), (5, 1, 1, 1, 1), (6, 1, 1, 1, 1), where (1, 1, 1, 1, 1) represents all five dice landing on a 6.
The answer is 7776 possibilities.
Order of the dice does not Matter
Now if 1, 1, 1, 1, 4 is the same as rolling a 1, 4, 1, 1, 1 then the problem is more complex. You can use the following formula (it's a binomial):
C(n+5, 5), where n is the amount of dice
C(5+5,5) = C(10,5)
How to use this:
C(A,B) = A! / [ (A-B)! B! ], where A! is read A factorial
What is a factorial:
n! = n x (n-1) x (n-2) ... x ... (n-n+1)
Example:
5! = 5 x (5-1) x (5-2) x (5-3) x (5-4)
5! = 5 x 4 x 3 x 2 x 1
Plug in your numbers;
C(10,5) = 10! / [ (10-5)! 5! ]
C(10,5) = 10! / ( 5! 5! )
( 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 ) / ( 1 x 1 x 2 x 2 x 3 x 3 x 4 x 4 x 5 x 5 )
= ( 6 x 7 x 8 x 9 x 10 ) / ( 2 x 3 x 4 x 5 ) = 30240 / 120 = 252 possibilities
The equation I gave you works for six sided dice problems. I have verified this answer numerically.
So the answers are:
7776 possibilities if order matters.
252 possibilities if order does not matter
What is the probability of rolling an odd number on 1 roll of die?
With a single die:
There are 6 sides on a dice.
There are 3 sides that are odd (1, 3, 5)
3/6 = 1/2 = 50%
Therefore, a single die has a 50% chance of landing on an odd number.
If you have two dice:
I'll explain this the longer way, however there are short (and simpler explanations) that basically use the fact that a single die is 50%, therefore two independent dice will also be 50%.
Number of dice = 2Sides of a dice = 6
Odd sides: 1, 3, 5, so Number of odd sides on a dice = 3
Even sides: 2, 4, 6, so Number of even sides = 3
Total combinations with two 6 sided dice = (sides on dice x sides on dice) = 6 x 6 = 36
We need to take the fact that:
An odd number + an odd number = even
An even number + an even number = even
An odd number + an even number = odd <--- we want this case
Odd combinations on a dice:
First dice is even, second dice is odd (even sides x odd sides):
(3) x (3) = 9
First dice is odd, second dice is even (odd sides x even sides):
(3) x (3) = 9
Total odd combinations:
9 + 9 = 18
Divide odd combinations by total combinations to get the probability:
18 / 36 = 1/2
You have a 50% chance to roll an odd number on a single roll of two six sided dice.
18 can.
What does districts must be compact contiguous and substantially equal in population mean?
It means that Gerrymandering is less easy.
Compact: Think of dropping a big spoonful of honey on a table. The result will be a round blob. We would say that the area of contact between the honey and the table is compact. In contrast, if you were to drop a spoonful of water from a couple of inches above the table it would splash out. There would be 'arms' of water that would spread out from the central wet area on the table. The area of contact between the water and the table would not be considered compact.
Contiguous: The city of New York is not contiguous. There's the mainland and there's Long Island, and these pieces are separated by salt water. In contrast the state of Idaho is contiguous--because it's all one big area.
Equal in population: obvious.
What is the probability of drawing a jack and a king?
The probability of drawing a jack and a king in that order from a standard deck is: P(J,K)
=
(4/52)∙(4/51) =
0.006033... ~ 0.006 ~ 0.6%
The probability of drawing a jack and a king in any order is twice the above:
P((J,K)
or (K,J)) =
0.0112066... ~ 0.011
~ 1.1%
Is rolling an even number on a number cube an outcome or an event?
Rolling a dice and getting an even number is an outcome. It is the result of rolling a dice.
