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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 the next four births at a hospital being all girls?
Assuming that the births at the hospital are equally likely to be of either gender then the answer is (1/2)4 = 1/16
The probability is 1.
What is the probability of rolling a 1 or 6 on a number cube and flipping tails on a coin?
The probability of flipping tails on a perfect coin in a perfect toss is 0.5.
The probability of rolling 1 on a die is 1 in 6.
Likewise, the probability of rolling 6 on a die is 1 in 6.
So the probability of rolling either 1 or 6 is 2 in 6 (which is 1 in 3).
What is the probability of not getting an even number on the spinner?
It depends on the spinner: how many sides it has, whether or not they are the same size, what numbers are on the spinner.
What are the odds against drawing a 3 out of a deck of 52 cards?
Of the 52 cards, 48 are not a 3, so the odds are 48/52 (which is 12/13).
Why does the standard error become smaller simply by increasing the sample size?
Because of the Law of Large Numbers. According to that law, the observations tends towards the mean. This increases the concentration of observations nears the mean thereby reducing the variance or standard error.
Which chamber of the heart has the highest probability of being the site of myocardial infarction?
left ventricle
What is the Difference between random and systematic sampling?
Random sampling is picking a subject at random. Systematic sampling is using a pattern to pick subjects, I.e. picking every third person.
What is the chance if you toss a pair of dice you get 6 for the sum?
Answer: 1/12 3+3
4+2
5+1
All the above equal six. There are 36 (6x6) different options so you get 3/36. 3/36 can be simplified into 1/12 (3/3 and 36/3). Therefore your answer is 1/12
The chance is five out of thirty-six or about 13.89%.
How are the mean and standard deviation affected by an outlier?
The mean is "pushed" in the direction of the outlier. The standard deviation increases.
Simple random sampling.
When two dice are rolled what is the probability of getting a sum of 5 or 6?
When two dice are rolled, the probability of getting:
2 is 1/36
3 is 2/36
4 is 3/36
5 is 4/36
6 is 5/36
7 is 6/36
8 is 5/36
9 is 4/36
10 is 3/36
11 is 2/36
12 is 1/36
Why is the standard error a smaller numerical value compared to the standard deviation?
Let sigma = standard deviation.
Standard error (of the sample mean) = sigma / square root of (n), where n is the sample size. Since you are dividing the standard deviation by a positive number greater than 1, the standard error is always smaller than the standard deviation.
What does it mean when the standard error value is smaller than the standard deviation?
It simply means that you have a sample with a smaller variation than the population itself. In the case of random sample, it is possible.
If the digit 0 is allowed then the answer is 1/(10*9*8) = 1/720 = 0.0014 approx.
If 0 is disallowed, then 1/(9*8*7) = 1/504 = 0.0020 approx.
What is the probability of obtaining 2 ones in a row when rolling a fair six sided die?
If you roll the die often enough, the probability of getting a 2 ones in a row is 1.
In only 2 rolls, the answer is (1/6)*(1/6) = 1/36
What is the probability of not rolling a number larger than 4 with a fair die?
The probability of not rolling a number larger than 4 is the probability of rolling a
number equal to 4 or lower: P(x≤4) = P(1) + P(2) + P(3) + P(4) = 4/6 = 2/3 =
0.6666... ≈ 66.7%
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.
