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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 best definition of probability?
the extent to which something is probable; the likelihood of something happening or being the case.
the chance that something will happen
the likelihood of an event occurring
What is the probability of a coin landing on heads when it is flipped 100 times?
The probability of landing on heads at least once is
1 - (1/2)100 = 1 - 7.9*10-31 which is extremely close to 1: that is, the event is virtually a certainty.
Not knowing exactly what the 'increase' is, it is hard to answer this. Here is what happens if the event probability is the same each time (at the bottom is one example where probability increases):
Let p = probability that the event will occur on a trial (attempt).
Let q = probability against the event occurring on a trial = 1 - p. [100% - probability for]
Probability that the event will not occur on n trials = qn, so the probability that the event will occur at least once on n trials is 1 - qn = 1 - (1-p)n.
Example: Say you roll a 6-sided die twice and want the probability that you'll get a 1 at least one of the throws.
p = 1/6, n = 2 : Probability = 1 - (1 - 1/6)² = 30.56%
Let's look at another way to figure this. Rolling a die twice, it's easy enough to make a 2-dimensional table of the results. There are 36 possibilities, and 11 of them have a 1 occurring. So the probability is 11/36 = 30.56%
If you were to do 3 attempts, you would have a 3-dimensional table with 216 possibilities, and 91 of them have a 1 occurring at least once.
91/216 = 42.13%, which is the same using the formula: 1 - (1 - 1/6)³ = 42.13%
So for the problem where the probability increases each time. As an example, say you're playing BINGO with 75 balls. Say you're playing a blackout game and 50 balls have already been drawn, and you've filled your block except for a single square (say it's number 1). So there are 25 balls remaining. It will be similar to above, except you cannot just square or cube the probabilities because they change.
You still want to calculate the probabilities against, then multiply them together then subtract from 100%. Since this is an example, you're playing BINGO and you look around at several neighbors and see that everybody around you has three spaces to fill, so you want to hit #1 in the next three balls.
Assign the probabilities for picking #1 on each trial as p1, p2, p3.
So p1 = 1/25. If you don't draw #1 the first time, then there are only 24 balls left, so p2 = 1/24, and p3 = 1/23. We need to multiply the q's (probabilities against) then subtract that product from 100%.
So the probability of drawing #1 on any of the next 3 trials, starting with 25 balls is: 1 - ((1 - 1/25)(1 - 1/24)(1 - 1/23))= 1 - ((24/25)*(23/24)*(22/23)) = 12%. Notice the way I wrote it, the fractions cancel. Here's the interesting thing:
The probability of getting #1 on the first try is 1/25 = 4%. The first or second try is 1 - ((24/25)*(23/24)) = 2/25 = 8%. Each trial will become an increased number over 25: 3/25 = 12%, 4/25 = 16%, etc. I'm not sure how you would generalize the formula though.
What is a sample that that consists of everyone in the population?
It is not a sample. A sample must be a proper subset of the whole population.
How do you find the probability of two distincve events?
It depends on whether or not the events are independent.
Fifty cards.
Fifty cards.
Fifty cards.
Fifty cards.
What happens in the event of a vacancy occurring in either chamer of congress?
== == the govenor appoints someone the govenor appoints someone
What are some probable preoperative diagnosis for a vulvectomy?
Vulvar cancer is the typical diagnosis.
50:50
0.48
Each question is an independent event with 4 possibilities, so the possibilities are 48 = 65,536
How do you ride a bike on ice easily?
Get a pair of studded tires.
Go steadily and easily but you can go fast if you are steady and a good bike handler. Give it a shot it is fun.
What does the 2 percent tornado probability from the spc typically mean?
A 2 percent tornado probability typically means that isolated and probably weak tornadoes are possible.
What is the probability of getting four consecutive twos from tossing a fair number cube?
The probability of the first one is 1/6 .
The probability of the second one is 1/6 .
The probability of the third one is 1/6 .
The probability of the fourth one is 1/6 .
The probability of all four is (1/6)4 = 0.0007716 (rounded) = 0.077 %
What is the probability is of getting 3 heads in a row if I toss the coin 10 times?
The probability of getting 3 or more heads in a row, one or more times is 520/1024 = 0.508
Of these,
the probability of getting exactly 3 heads in a row, exactly once is 244/1024 = 0.238
How do you get Goku's powers in real life?
You can't get his powers but you can make it look real. Step1:get a video camera and act like Goku when he is doing an Techniche, Step2: make sure it was recorded otherwise hit the record button and do it again, Step3:take the recorded video edit it to where it looks like it was real so basicly go to paint and draw on a picture of the techniche, Step4:If you have a Youtube account (if you don't have one go make it on Youtube.com) save the video and upload it to Youtube. I tried it myself and it actualy worked!
0.63 = 0.216
The probability of obtaining exactly two heads in three flips of a coin is 0.5x0.5x0.5 (for the probabilities) x3 (for the number of ways it could happen). This is 0.375. However, we are told that at least one is a head, so the probability that we got 3 tails was impossible. This probability is 0.53 or 0.125. To deduct this we need to divide the probability we have by 1-0.125
0.375/(1-0.125) = approximately 0.4286
What are the uses of Normal Distribution?
The normal distribution is very important in statistical analysis. A considerable amount of data follows a normal distribution: the weight and length of items mass-produced usually follow a normal distribution ; and if average demand for a product is high, then demand usually follows a normal distribution.
It is possible to show that when the sample is large, the sample mean follows a normal distribution. This result is important in the construction of confidence intervals and in significance testing. In quality control procedures for a mean chart, the construction of the warning and action lines is based on the normal distribution.
How many people study Hinduism right now?
There are an estimated one billion people who profess to study some aspect of Hinduism as of 2013. This number has increased dramatically over the last ten years.
What is the probability of drawing 2 spades from a deck of 52 cards?
If you just draw two cards, 1/13 times 1/12
i.e. 1/156
What is the probability of a prime number being picked randomly from the numbers 1 through 49?
There are 15 primes from 1 to 49 (including '1').
The probability is (15/49) = 30.612 %(rounded)
What is the probability of picking 6 ball from 99?
events are 99
events wanted 6
so probability is 6/99
