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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

What is the distribution of area under a curve?

In terms of probability theory, the cumulative distribution function (cdf) is the result of the summation or integration of the probability density function (pdf). The cdf F(a) is the area under the pdf from its lower limit to a. I hope I am responding to your question. If not, perhaps you can clarify it and resubmit it.

The variance for the binomial probability distribution is?

n(p)(1-p) n times p times one minus p, where n is the number of outcomes in the binomial distribution, and p is the probability of a success.

What is probability of union and probability of intersection?

probablity of union

probabilty of union is define as

P(AUB)=P(A)+P(B)-P(AnB) (for not mutualy exclusive data( where atleast one event

is common in two samples)

P(AUB)=P(A)+P(B) (mutualy exculsive)

probablity of intersect

P(AnB)=P(A).P(B)

If you roll one die with 6 sides what is the probability that you will roll a 3 or a 4?

The answer is 1/3. There are six possible outcomes (1 to 6) of which two (3 or 4) are favourable so the probability is 2/6 or 1/3. In general, if A and B are two events, then Pr (A or B) = Pr(A) + Pr(B0 - Pr(A and B) [the last bit is because you are double counting those events] Here Pr(A) = Pr(3) = 1/6, Pr(B) = Pr(4) = 1/6 and Pr(A and B) = Pr(3 and 4 - simultaneously) = 0 So Pr(3 or 4) = 1/6 + 1/6 + 0 = 1/3

What is sample space for tossing 2 coins?

The sample space for tossing 2 coins is (H = Heads & T = Tails): HH, HT, TH, TT

Toss a coin 3 times and what is the probability of getting at least two heads?

There are 23 or 8 possible outcomes listed below (H=Head, T=Tails). HHH HHT HTH HTT THH THT TTH TTT each has a 1/8 probability. Count the number that has at least 2 heads and it is 3. So, the probability is 3/8.

If two dice are thrown what is the probability of the sum of the numbers being a seven or an eleven?

To roll a 7, it doesn't matter what your first die rolls at, as every number on the die has a complement that will add up to 7. This means that your odds on rolling 7 are actually your odds on rolling the appropriate number on the second die. ie. 1/6. No matter what your first die is, the second can potentially give you a number that brings the total to 7.

To roll an 11 however, your odds are not as high. This is because you must roll a five and a six to hit 11. Your first die can be either of the two, but your second die must be it's complement. In this case then, your odds are 2/6 * 1/6, or 1/18.

Two events A and B with probability 0.5 and 0.7 respectively have joint probability of 0.4 The probability that neither A nor B happens is?

Let me denote -A as the event that A does not happen. So we want Pr[-(A and B)]

Now, the event that neither A nor B occurs is the opposite of either A occurring, or B occurring or both occurring.

So Pr[-(A and B)] = 1 - Pr(A or B)= 1 - [Pr(A) + Pr(B) - Pr(A and B)] (since A+B is double counted)= 1 - (0.5 + 0.7 - 0.4)= 1 - 0.8= 0.2

If the overall percentage of success in exam is 60 .what is probability that ouit of group of 4 students.at least one has passed?

This is a Binomial Probability Distribution; n=4, p=0.6. The probability of at least 1 passed is equal to the probability of 1-none passed; so x=0. The probability of x=0 (with n=4, p=0.6) is 0.0256. So, the probability of at least 1 passed is 1-0.0256 or 0.9744.

Where are the Twenty five Spades in you spy Super Challenger?

well the first 12 is in box number 10 the second is in box number 9 and it has 9 spades the third is in box number 2 and it has 4 spades and that's all 25 of them

A die is loaded so that the number 6 comes up three times as often as any other number What is the probability of rolling a 1 or a 6?

If you roll the die one time, there is a 1/3 probability that you will get a 1 or a 3.

There are 6 possibilities: 1,2,3,4,5,6-----> This number goes on the bottom of your fraction because it is what the probability is out of.

You want 2 different numbers: 1,6--------> This goes on the top because those are the 2 numbers you want.

So the fraction (probability) is 2/6, which simplifies to 1/3.

Probability of getting all questions wrong on multiple choice test?

In order to answer, the number of questions on the test must be given.

How do you calculate two standard deviations of the mean?

See the related links on how to calculate standard deviation. If there are more than a dozen data points, it is tedious to calculate by hand. Use excel or an online calculator. To get 2 standard deviations, multiply the calculated std deviation by 2.

What is the probability of getting a number less than 3 in two tosses of a single die?

In single die,

S = {1,2,3,4,5,6} So n(S) = 6

The event A is defined as getting a number less than 3.

A = {1,2} So n(A)=2

Hence P(A) = n(A)/n(S) = 2/6 =1/3

What is the standard deviation for 3 5 12 3 2?

From the online calculator, see related link, the standard deviation is 4.06202.