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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 probability of a girl being chosen if there are 10 boys and 14 girls?

If the choice is unbiased, the change is 14/(10+14).

If the chooser prefers choosing boys, the probability is 0.

How many combinations can you make with 5 letters when letters can be repeated?

7,893,600 (seven million, 8 hundred ninety-three thousand, 600) combinations in English.

What is measured by the numerator of the z-score test statistic?

The z-score, for a value z, is the probability that a Standard Normal random variable will have a value greater than z.

What is the probability of getting two kings and two ace that are all diamonds?

Since there are two kings of diamond (and two aces of diamond), there are more than one decks of cards. However, you have chosen not to say how many decks are involved. Nor do you mention whether the cards are replaced before the next card is picked. Without this information it is not possible to answer the question.

What is an example of relative frequency probability?

Flip a coin 1000 times, counting the number of 'heads' that occur. The relative frequency probability of 'heads' for that coin (aka the empirical probability) would be the count of heads divided by 1000. Please see the link.

If a single die is rolled 9 times what is the probability of getting exactly 2 sixes?

There are 69 total possibilities.

Imagine having nine boxes, that each hold how many possibilities each individual dice can hold. Any two of the dice can only be a six, therefore any two of the boxes can only have a 1 (only one possibility). The rest of the boxes can be anything, other than 6 (so the rest of the boxes have 5 possibilities each).

[1] [1] [5] [5] [5] [5] [5] [5] [5]

Now multiply all the possibilities together you get total number of combinations. In this case, it's 57. You can use this same strategy to see why the total number of possibilities is 69.

The answer is total restricted combinations divided by total combinations.

57 / 69 ~= 0.007752 (or roughly 0.78%)

What is the relative frequency of score less than 120 using the 68-95-99.7 rule if a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20?

120 is one standard deviation greater than the mean (z = 1).

So you want Pr(z < 1)

The probability of a score at most 1 sd away from the mean is 0.68

That is Pr(-1 < z < 1) = 0.68

So Pr(|z| > 1) = 1 - 0.68 = 0.32

then by symmetry,

Pr(z > 1) = 1/2*0.32 = 0.16

So Pr(z < 1) = 1 - 0.16 = 0.84

120 is one standard deviation greater than the mean (z = 1).

So you want Pr(z < 1)

The probability of a score at most 1 sd away from the mean is 0.68

That is Pr(-1 < z < 1) = 0.68

So Pr(|z| > 1) = 1 - 0.68 = 0.32

then by symmetry,

Pr(z > 1) = 1/2*0.32 = 0.16

So Pr(z < 1) = 1 - 0.16 = 0.84

120 is one standard deviation greater than the mean (z = 1).

So you want Pr(z < 1)

The probability of a score at most 1 sd away from the mean is 0.68

That is Pr(-1 < z < 1) = 0.68

So Pr(|z| > 1) = 1 - 0.68 = 0.32

then by symmetry,

Pr(z > 1) = 1/2*0.32 = 0.16

So Pr(z < 1) = 1 - 0.16 = 0.84

120 is one standard deviation greater than the mean (z = 1).

So you want Pr(z < 1)

The probability of a score at most 1 sd away from the mean is 0.68

That is Pr(-1 < z < 1) = 0.68

So Pr(|z| > 1) = 1 - 0.68 = 0.32

then by symmetry,

Pr(z > 1) = 1/2*0.32 = 0.16

So Pr(z < 1) = 1 - 0.16 = 0.84

What are the 4 probabilities?

There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.

There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.

There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.

There are not just 4 probabilities. Probability is a continuous variable ranging from 0 to 1: it can take infinitely many values.

What is the probability of spinning a number greater than 5 or less than on this spinner?

The answer depends on the spinner: how many sides it has and how they are numbered. These details are not given in the question and so there is no way to answer the question.

The answer depends on the spinner: how many sides it has and how they are numbered. These details are not given in the question and so there is no way to answer the question.

The answer depends on the spinner: how many sides it has and how they are numbered. These details are not given in the question and so there is no way to answer the question.

The answer depends on the spinner: how many sides it has and how they are numbered. These details are not given in the question and so there is no way to answer the question.

What examples are there for a theoretical probability of 100?

No probability - theoretical or not - can be 100. Therefore no examples are possible.

No probability - theoretical or not - can be 100. Therefore no examples are possible.

No probability - theoretical or not - can be 100. Therefore no examples are possible.

No probability - theoretical or not - can be 100. Therefore no examples are possible.

What is the Greek root of probability?

Probability is derived from Latin, not Greek.

Probability is derived from Latin, not Greek.

Probability is derived from Latin, not Greek.

Probability is derived from Latin, not Greek.

What is the mean absolute deviation of the bowling scores?

This question cannot be answered unless the bowling scores are provided.

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