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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
Can you have a z score above 3?
Yes.
However, a z-score greater than 3 implies either that the outcome is rare (prob = 0.135%) or that some of the assumptions regarding the variable are incorrect. This could be the distribution itself or its parameters.
What is the probability of picking a diamond out of a 52 card deck of cards?
The probability of picking a diamond out of a standard deck of 52 cards is 13 in 52, or 1 in 4, or 0.25.
1\12
What is the probability of drawing the 7 of diamonds if you dont return the card?
The probability of drawing any single card in a deck of 52 cards is 1 in 52. It does not matter if you replace it or not, unless you intend to make multiple draws.
In the multiple draw case, each subsequent probability increases; 1 in 51, then 1 in 50, then 1 in 49, etc.
As an example, the probability of drawing the seven of diamonds in five draws from a standard deck is 1 in 52 plus 1 in 51 plus 1 in 50 plus 1 in 49 plus 1 in 48. This adds up to about 1 in 10.
What is the number of distinguishable permutations of the letters in the word oregon?
360.
There are 6 letters, so there are 6! (=720) different permutations of 6 letters.
However, since the two 'o's are indistinguishable, it is necessary to divide the total number of permutations by the number of permutations of the letter 'o's - 2! = 2
Thus 6! ÷ 2! = 360
How is standard deviation different from mean absolute decation?
If I have understood the question correctly, despite your challenging spelling, the standard deviation is the square root of the average of the squared deviations while the mean absolute deviation is the average of the deviation.
One consequence of this difference is that a large deviation affects the standard deviation more than it affects the mean absolute deviation.
The requirement that one coin is a head is superfluous and does not matter.
The simplified question is "what is the probability of obtaining exactly six heads in seven flips of a coin?"...
There are 128 permutations (27) of seven coins, or seven flips of one coin. Of these, there are seven permutations where there are exactly six heads, i.e. where there is only one tail.
The probability, then, of tossing six heads in seven coin tosses is 7 in 128, or 0.0546875.
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.
How many ways can you get a sum 4 when rolling a pair of dice?
two ways
one and three
and a pair of twos
What is the difference between discrete and cumulative distributions?
A discrete distribution is one in which the random variable can take only a limited number of values.
A cumulative distribution, which can be discrete of continuous, is the sum (if discrete) or integral (if continuous) of the probabilities of all events for which the random variable is less than or equal to the given value.
Are mutually exclusive events also complementary events?
Not necessarily. The probability of a complementary event with probability p is 1-p. Two mutually exclusive events, however, don't necessarily add up to a probability of 1.
For example, the probability of drawing a King from a standard deck of cards is 1 in 13, which the complementary probability of not drawing a King is 12 in 13.
The probability, however, of drawing a Heart is 1 in 4, while the probability of drawing a Club is also 1 in 4. That leaves Diamonds and Spades, which account for the remaining probability of 2 in 4.
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 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.
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 probability landing on a 3?
land on a 3? as in a dice? well if so then it is 1/6 chance because there are 6 numbers on a dice and 3 is one of them so 1/6
How many possible outcomes exist when rolling a number cube that has sides that say 3 5 and 6?
Three: they are 3, 5 and 6.
Seven coins are tossed What is the probability of 3 heads or 2 tails?
The probability of one event or the other occurring is the probability of one plus the probability of the other. The probability of getting 3 heads is the probability of 3 heads (1/23) multiplied by the probability of 4 tails (1/24) multiplied by the number of possible ways this could happen. This is 7c3 or 35. Thus the probability of 3 heads is 0.2734375. The probability of 2 tails is the probability of 2 tails (1/22) multiplied by the probability of 5 heads (1/25) multiplied by the number of ways this could happen. That is 7c5 or 21. Thus the probability of 2 tails is 0.1640625
The probability of one or the other is the sum of their probabilities:
0.1640625 + 0.2734375 = 0.4375
Thus the probability of getting 3 heads or 2 tails is 0.4375.
What is the shape of the distribution of the mean of a sample?
The mean of a sample is a single value and so its distribution is a single value with probability 1.
What is the probability of rolling a sum of 8 and doubles when rolling two dice?
The probability of rolling a sum of 8 and doubles when rolling two dice is 1 in 36, or about 0.02778.
Simply note that there are 36 permutations of two dice, of which exactly one of them (a 4 and a 4) matches the conditions specified.
