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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 having the same number when rolling a dice twice?
If it is a regular dice then the probability is 3/6 that is 1/2
First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.
A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.
It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.
Or, of course, it could be a mixture of both.
First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.
A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.
It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.
Or, of course, it could be a mixture of both.
First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.
A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.
It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.
Or, of course, it could be a mixture of both.
First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.
A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.
It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.
Or, of course, it could be a mixture of both.
It is the number of elements in the sample. By contrast, the relative sample size is the absolute sample size divided by the population size.
What are the odds of getting the same number on an 8 sided die four times in a row?
(1/8)3, or about 0.001953.
I raised one eighth to the third power, instead of the fourth power, because you are really asking the odds of matching one of the rolls, leaving three rolls in which to do so.
What the difference and relationship between a probability distribution and a probability function?
They are the same. The full name is the Probability Distribution Function (pdf).
a number wich disproves a proposition For example, theprime number 2 is a counterexample to the statement "All prime numbers are odd."
(1/2) * (1/6) = 1/12
What is theoretical and experimental?
Theoretical refers to a proposition derived on the basis of the laws of science whereas experimental refers to those derived from experiments or trials.
Theoretical refers to a proposition derived on the basis of the laws of science whereas experimental refers to those derived from experiments or trials.
Theoretical refers to a proposition derived on the basis of the laws of science whereas experimental refers to those derived from experiments or trials.
Theoretical refers to a proposition derived on the basis of the laws of science whereas experimental refers to those derived from experiments or trials.
The answer depends on what proportion you want the expected value for.
Is variance based on deviations from the mean?
Variance is the squared deviation from the mean. (X bar - X data)^2
Suppose X = sum
Pr(X = 3n where n is an integer or X>4)
= 1 - Pr(X ≠3n and X ≤ 4)
= 1 - pr(X = 2 or X = 4) since these are the only two outcomes that meet the requirements of the event.
= 1 - [Pr(X=2) + Pr(X=4)]
= 1 - [1/36 + 3/36]
= 1 - 4/36 = 1 - 1/9
= 8/9
What do you think might happen if you rolled the die 500 times?
If you rolled that many times, you'd have approximately the same number of each - however many sides your die had. It's totally random, but it'll average out so that each number comes up about the same number of times. It's not going to be exact (like 50 #1s and 50 #2s and 50 #3s and so on) but it will average out to be about the same.
How many number of bits are required to permit selection of 1 out of 32 equi-probable events?
5 bits, since 2 to the power 5 equals 32.
How many ways can 5 people sit in a row if 2 of them insist on not sitting together?
The first thing to do is to work out how many ways there are without those 2 people minding. There are 5 possibilities for first place, 4 for second and so on, so the number of ways is 5x4x3x2x1 = 120.
The next step is to work out how many of these possibilities have the two people sitting next to each other. There are 4 ways in which two people can sit next to each other. For each of these ways there are two possibilities, one with one person on the right, and the other with them on the left. For each of these 8 ways, there are 3x2x1=6 ways the other people could have sat. So there are 8x6=48 invalid ways in total.
120-48 = 72
So there are 72 ways 5 people can sit in a row if 2 of them insist on not sitting together.
What is the sketch for a normal distribution?
The normal distribution is a bell shaped curve. Properly normalized, the area under the curve is 1.0. Start by drawing axes. The Y axis is probability, peaking at 0.4, crossing the X axis at the mean, and the X axis is standard deviation. Draw points (-3, 0.01), (-2, 0.05), (-1, 0.25), (0, 0.4), (+1, 0.25), (+2, 0.05), (+3, 0.01). These are all approximations. Connect the dots, understanding that the curve is asymptotic to the X axis.
For a better picture, as well as an explanation, please see the related link below. This picture also shows you the percentage each area, grouped by standard deviation, or sigma, is. The normal distribution is the second picture on the right. Scroll up to see the picture, call "Normal Distribution".
In heads and tails why is is mostly tails?
Is it?
Let's say you flip a coin three times, and it comes up tails each time. You may state that from your experience, tails is preferred overwhelmingly.
But three tails is likely to occur approximately 12% of the time, and three heads also will occur 12% of the time.
So, instead of asking why coin flips are biased to the tails, perhaps it is better to ask what evidence exists showing that one side is more likely to occur than another. I couldn't find any. I attach the link on coin flips.
In other words you will never know unless of course you count the seconds its in the air and look what side it lands on. That always works.
You are dealt a 5-card hand from a deck of 52 cards. Let event F equal "all the cards in your hand are from the same suit" and let event S equal "the numbers of your cards form an uninterrupted sequence."
Which of the following hands are contained in the event F
