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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
50%
Why is the probability of intersection of two events subtracted in the sum of the events?
The short answer is that if you don't do so, the intersection is double counted. The longer answer follows:
Suppose you have two events A and B which overlap. Then,
Event A = (only A happens) and (both A and B happen).
These two are mutually exclusive so that P(A) = P(A only) + P(both).
Similarly, P(B) = P(B only) + P(both).
Now, the event that A or B happen is the event that only A happens or only B happens or both happen.
That is, P(A or B) = P(A only) + P(both) + P(B only)
Adding and subtracting P(both) gives
P(A or B) = P(A only) + P(both) + P(B only) + P(both) - P(both)
Now, the first two are P(A) and the next two are P(B)
So P(A or B) = P(A) + P(B) - P(both).
How do you get the median of a continuous random variable?
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
What is the probability of rolling two 2's on two six-sided die?
The chance is 1/36.
(There are 36 possible combinations for two 6-sided dice, but only 18 separate combinations when the dice are not considered seperately.)
How can you simplify 31 over 36?
Well, honey, simplifying 31 over 36 is like trying to fit into your high school jeans after Thanksgiving dinner. You just divide the top and bottom by the greatest common factor, which in this case is 1. So, 31 over 36 stays as is because there's no simpler way to write it.
What is the purpose of doing the z-score?
The Normal distribution is frequntly encountered in real life. Often a matter of interest is how likely it is that the random variable (RV) being studied takes a value that it did or one that is more extreme. This requires a comparison of the observed value of the RV with its Normal distribution. Unfortunately, the general Normal distribution is extremely difficult to calculate.
The Normal distribution is defined by two parameters: the mean and the variance (or standard deviation). It is impossible to tabulate the distribution of every possible combination of two parameters - both of which are continuous real numbers. However, using Z score reduces the problem to that of tabulating only one the Normal distribution: the N(0, 1) or standard Normal distribution. This allows the analysis of an RV with any Normal distribution.
When you roll four dice how many different number combinations could you roll that will total 14?
There are 8 different combinations.
There are 145 permutations that total 14.
Not asked, but answered for completeness sake; there are 1296 possible permutations of four dice, making the probability of a sum of 14 being 145 in 1296 or about 0.1119.
the normal distribution is a bell shape and expeonential is rectangular
There are 16 trials.
When two dice are rolled Fine the odds that the score on the dice is either 3?
To roll a three on any one dice, the odds are 1/6. To roll a three on any one of a pair of dice, the odds are 1/6 x 1/6 which is 1/36 or 1 in 36 chance.
What is the probability of getting a sum 9 from two throws of a dice?
There are 36 permutations of two dice.1 Of these 4 have a sum of 9, specifically 36, 45, 54, and 63. Therefore, the probability of throwing a sum of 9 on two dice is 4 in 36, or 1 in 9, or about 0.1111.
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1It does not matter it you throw one die two times or two dice once. Since these are independent events, the probabilities are the same either way.
None.
z-scores are linear transformations that are used to convert an "ordinary" Normal variable - with mean, m, and standard deviation, s, to a normal variable with mean = 0 and st dev = 1 : the Standard Normal distribution.
What is the z-score for a test score of 110?
In order to know the z-score, given a test score, you must also know the mean and the standard deviation. Please restate the question.
How many distinguishable permutations are there of the letters in the word effective?
The number of permutations of the letters EFFECTIVE is 9 factorial or 362,880. To determine the distinct permutations, you have to compensate for the three E's (divide by 4) and the two F's (divide by 2), giving you 45,360.
The cumulative probability up to the mean plus 1 standard deviation for a Normal distribution - not any distribution - is 84%. The reference is any table (or on-line version) of z-scores for the standard normal distribution.
When two dice are rolled find the probability of getting a sum of greater than 15?
Two standard dice cannot have a sum greater than 12. The probability, then, of getting a sum greater than 15 is zero.
How do you find experimetal probability?
Experimental probability is calculated by taking the data produced from a performed experiment and calculating probability from that data. An example would be flipping a coin. The theoretical probability of landing on heads is 50%, .5 or 1/2, as is the theoretical probability of landing on tails. If during an experiment, however, a coin is flipped 100 times and lands on heads 60 times and tails 40 times, the experimental probability for this experiment for landing on heads is 60%, .6 or 6/10. The experimental probability of landing on tails would be 40%, .4, or 6/10.
What is the probability of getting an even number on a dice?
3/6 or 50%. if simplified it would equal 1/2.
What is the probability of getting three heads in a row if you flip a coin five times?
Each flip can land in 2 ways. Total number of possible ways that 5 flips can land is
2 x 2 x 2 x 2 x 2 = 32 different ways.
There are only 5 different ways to get exactly 3 heads in a row in 5 flips.
They are:
H H H T T
H H H T H
T H H H T
T T H H H
H T H H H.
The probabilty is 5/32 = 15.625 percent.
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That's if you mean exactly 3 heads in a row ... no less and no more.
What if you asked for "at least 3 heads in a row" ?
There are 8 ways to do that:
The original five ways to get 3 in a row . . .
H H H T T
H H H T H
T H H H T
T T H H H
H T H H H
Plus 2 ways to get 4 in a row . . .
T H H H H
H H H H T
Plus a way to get 5 in a row . . .
H H H H H.
The probability of one of these outcomes is 8/32 = 25 percent.
