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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 two unprecedented events occurred in connection with the ERA voting?
The first event was that when the ERA did not get ratified in its seven year limit, Congress extended ratification time by three extra years. The second event was that even though the deadline was extended the bill did not get ratified, and five states even tried to take back their votes.
What is the probability of rolling a die and getting a 3 the first time?
There are 6 sides on a die, so the denominator should be 6. The number 3 appears on the dice once, so the fraction probability should be 1/6.
What is the probability of a composite number if you rolled a six sided dice?
The probability of rolling a composite number on a 6 sided die, numbered 1, 2, 3, 4, 5, and 6, is 1 in 3.
There are two composite numbers on the die, 4 and 6. The others are prime, 2, 3, and 5, or unity, 1, so there are 2 possible outcomes in an possible result set of 6, hence the probability is 2 in 6, or 1 in 3.
Suppose a population consisted of 20 items How many different samples of n equals 3 are possible?
There are 20 ways to choose the first sample, which leaves 19 ways for the second one, and 18 for the third one. So (apparently) there are 20 x 19 x 18 ways to choose a sample of 3 items, BUT, since the order of choosing a particular set of 3 doesn't matter, we need to divide by 3 x 2 x 1; so the final calculation is (20 x 19 x 18) divided by (3 x 2 x 1). Cancelling by the 3 and the 2 we have 10 x 19 x 6 = 10 x 114 = 1140
Probability of 3 marbles 2 yellow and 4 red in a bag?
The probability depends on the availability of marbles of those colours to the person making up the bag.
What important events occurred during 2009?
See related link. Other people may not view the same events as important.
Yes.
How can you use perpendicular and angle bisectors to form a 45 degree angle?
You draw a perpendicular at the end of a line segment. You then bisect the right angle formed between the original line and the perpendicular. The resulting angle will be 45 degrees.
There are two possible sums that add up to a number evenly divisible by 2 and 3, namely 6 and 12.
There are 5 different ways to roll a sum of 6, so the probability of that happening is 5/36.
There is 1 way to roll a sum of 12, so the probability of that happening is 1/36.
The probability of either happening is the sum of the two separate probabilities.
p=5/36+1/36=6/36=1/6 ~= .1667 = 16.67%
Does the size of the standard deviation of a data set depend on where the center is?
Yes it does. The center, which is the mean, affects the standard deviation in a potisive way. The higher the mean is, the bigger the standard deviation.
Would a small deviation in an experiment mean that something is wrong with the experiment?
Not necessarily. It might mean that the experiment has a highly stable outcome. You need to evaluate if that is true or if the experiment is flawed. It comes down to theoretical expectations versus experimental outcomes - you should know a priori (before the fact) what to expect, so you can know if the results are good.
For instance...
If you were measuring the radioactivity of a sample with a relatively low count rate using a detector that recorded counts in each second, you would expect a poissen distribution.
If you were measuring the same sample with a detector that counted for 1 minute, you would expect a more gaussian distribution.
If, on the other hand, you were measuring the wavelength of a red laser, you would expect that every single observation would give you the same results, within an extremely tight distribution.
What does denominator of z-score measure?
The standard deviation.z-score of a value=(that value minus the mean)/(standard deviation)
Systematic sampling
What is the probability of a couple giving birth to five girls in a row?
Probability of girl, assumed to be 0.5. Therefore, probability of 5 girls is 0.5^5 or 0.03125.
A pair of dice are rolled What is the probability sum 12?
There is one way to roll a sum of 12.
There are 36 different outcomes from rolling a pair of dice.
Therefore, the probability is 1/36 ~= 0.0278 = 2.78%
What is the probability of tossing a coin 3 times and getting 3 heads?
There are 23 or 8 possibilities; one is HHH. So, probability of HHH is 1/8 or 0.125.
Does a parameter describe a population or a sample?
A parameter describes a population. A statistic describes a sample.
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
