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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 your parachute failing?
It depends on how well you pack it, how good a condition it is in, and on how correctly you use it.
In practice, the probability is very low. About one in every 100,000 jumps in the US results in a fatality, a probability of about 0.00001, but that's not just due to parachute failure. One unconfirmed estimate is that one in a thousand (0.001) main chute deployments result in a malfunction, but it is true that very few of those result in a fatality, primarily because there is a reserve chute that is maintained and packed under different, more stringent, requirements.
The 5th percentile of a standard normal distribution is -1.645 (from the normal probability table).
z = (x - μ) / σ
-1.645 = (x-98.2) / .62
(0.62)(-1.645) = x-98.2
-1.0199 = x-98.2
x = 98.2-1.0199 = 97.1801
The 5th percentile is 97.18
The 95th percentile of a standard normal distribution is 1.645 (from the normal probability table).
z = (x - μ) / σ
1.645 = (x-98.2) / .62
(0.62)(1.645) = x-98.2
1.0199 = x-98.2
x = 98.2+1.0199 = 99.2199
The 95th percentile is 99.22
Does spinning a four section spinner affect a six-sided number cube will land upon when tossed?
Presuming that the spinner and the number cube are both "fair", then no - spinning the spinner and tossing the six-sided number cube are called statistically independent events. They do not influence each other, and it does not matter which order the events occur in.
Pr(Sum > 25) = Pr(Spinner = 30 or 40 and Cube = 6)
= Pr(Spinner = 30 or 40)*Pr(Cube = 6)
= 2/4 * 1/6 = 1/2*1/6 = 1/12 or 8.33... %
What would be the chance of picking a multiple of 2 from a deck of cards?
If one card is picked at random from a normal deck of cards, the probability is 20/52 or 5/13.
What was the outcome of this event?
Could you please specify which event you are referring to? This will help me provide a more accurate and relevant answer.
Sampling errors are errors in the data collected during the carrying out of quantitative data surveys. They can occur for various reasons, e.g. surveys that were incorrectly filled out. It is generally said that a survey needs to have a margin of error of under 3% to be statistically significant.
What is differential calculus?
That is the part of calculus that is basically concerned about calculating derivatives. A derivative can be understood as the slope of a curve. For example, the line y = 2x has a slope of 2 at any point of the line, while the parabola y = x squared has a slope of 2x at any point of the curve.
4/52 = 1/13
There are 4 sixes (the numerator)
There are 52 cards (denominator)
Reduce your fraction
You have 4 chances out of 52 that the card you pick will be a six (because there are 4 sixes in the 52-card deck)
What are the features of a binomial distribution?
An experiment with only two outcomes ("success" and "failure"), a constant probability of success, a number of independent trials.
Then, if the probability of a success in a trial is p, the probability of r successes in n trials is
nCr*pr*(1-p)(n-r) for r = 0, 1, 2, ..., n.
In case the super-and sub-scripts do not work, that is
n!/[r!*(n-r)!]*p^r*(1-p)^(n-r)
What is the difference between double sampling and multiphase sampling?
DOUBLE SAMPLING
Definition:
A standard form of sample design for industrial inspection purposes. In accordance with the characteristics of a particular plan, two samples are drawn, n1 and n2, and the first sample inspected. The batch can then be accepted or rejected upon the results of this inspection or the second sample be inspected and the decision made upon the combined result.
Context:
The term has also been used somewhat loosely for what is called multi-phase sampling and the two-stage version of multi-stage sampling. There is a further usage whereby a first sample provides a preliminary estimate of design parameters which govern the size of the second sample to achieve a desired overall result.
MULTI-PHASE SAMPLING
Definition:
It is sometimes convenient and economical to collect certain items of information from the whole of the units of a sample and other items of usually more detailed information from a sub-sample of the units constituting the original sample. This may be termed two-phase sampling, e.g. if the collection of information concerning variate, y, is relatively expensive, and there exists some other variate, x, correlated with it, which is relatively cheap to investigate, it may be profitable to carry out sampling in two phases.
At the first phase, x is investigated, and the information thus obtained is used either (a) to stratify the population at the second phase, when y is investigated, or (b) as supplementary information at the second phase, a ratio or regression estimate being used.
Two-phase sampling is sometimes called "double sampling".
Context:
Further phases may be added if desired. It may be noted, however, that multiphase sampling does not necessarily imply the use of any relationships between variates x and y. The expression is not to be confused with multi-stage sampling.
It depends on how the game is structured, a piece of information that was not given in the answer...
If the numbers are reused, then there are 1 x 107 (ten billion, in the short scale) permutations. Without combinations, then, the probability is 1 x 10-7.
If the numbers are not reused, and we are playing combinatorial, in the style of most state sponsored lotteries, then the number of combinations is (10-3)! / 7!, which is 120, making the probability 1 in 120, or about 0.00833.
There are other possibilities but, again, it depends on the rules, and you did not specify them completely.
If a couple has five boys the chance that next child will be a boy is?
most likely 1 out of five chance
Explain how to estimate 498 divided by 12?
Let's see. Estimating would start with rounding up 498. 498 will turn into 500. Next, we round 12. Twelve rounds to 10, so it ends up to become 500 divided by 10. 500 divided by 10 is 50. So, estimated, 498 divided by 12 would be somewhere near 50.
(by the way, 498 divided by 12 is actually, non-estimated, 41.5.)
How do you work out the probability that a biased dice will land on a six is 0.35?
You roll it many times. The probability that it lands on a six is the number of times that it lands on a six divided by the number of times the die has been rolled.
Is 5 pounds of sugar bigger than 75 oz of chocolate?
5 x 16 = 80 oz sugar
so 5lb has more mass than 75 oz
What is the least common factor of 60 and 84?
The least common factor of any set of positive integers is 1.
