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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
Why do you have to perform many trials in probability experiments?
Probability determines likely outcomes, not what will happen every time. For instance, if you tossed a coin, the probabilty of coming up heads or tails is even, but there is also a vanishingly small possibility that it wil land on its edge.
If you only tossed the coin once, and it came up heads, you could not infer from that result that "if I toss a coin, it will come up heads." The next 10 tosses of the coin might come up heads, but if the experiment is run enough times, a roughly equal number of heads and tails would be observed.
This is true of any probability experiment. In biological experiments especially, because we are dealing with the unpredictability of living organisms, a watershed has to be determined, below which we can say with reasonable certainty that the probability of a particular outcome is less than, say 0.5%.
If you imagine a bell, the edges flare out, and it rises steeply to a shallow curve at the top. If we place the results of our repeated experiments under that bell, most will fit somewhere under the shallow part of the curve, with the results falling of rapidly to approaching 0 as the values move down to the flare. With just 1 or 2 results, it would be easy to get a distorted picture of a likely outcome.
What is the difference between population and parameters?
The population is a group of interest, such as the people who filled out a recent survey about their age. The parameter is the descriptive measure of that population. So in this example, a parameter could be the average age of the people who filled out the survey.
A clumped distribution indicates the resources are probably?
only available in certain spots
for Plato users the answer is D. patchy
What is the probability of throwing a total of six when you throw a pair of standard dice?
Possibilities for the first cube = 6 .
Possibilities for the second cube = 6 .
Possibilities for both cubes = 6 x 6 = 36 .
Ways to throw a total of 6 = 5 ways .
1 . 5
2 . 4
3 . 3
4 . 2
5 . 1
Probability of throwing a total of 6 = 5/36 = 138/9% .
What is the probability of not picking an ace out of a pack of cards?
If there is 52 cards the probability is 48/52 or 24/26 or 12/13
When tossing 5 coins simultaneously can you find the probability that at least 1 head is showing?
Probability not at least 1 head showing is when all 5 coins are tails: (1/2)5=1/32
Therefore probability at least 1 head is showing is 1-1/32=31/32
4 sided spinner spin 200 times probabilty it will land on side 2?
Probability that it will land on side 2 at least once = 1 - 0.75200 = which is around one in ten septillion (10-25) less than 1 ie a near certainty.
How to solve probability questions?
Count the total number of ways it can turn out.
Count the number of ways that are the condition you're looking for.
The probability of the outcome you're looking for is is the second number divided by the first number.
How many permutations can be made from selecting 4 college courses out of 10?
For first course there are 10 choices
for second 9
for third 8
for fourth 7
total choices of selecting = 10*9*8*7=5040
Is unimodal a normal distribution?
It may be or may not be; however a normal distribution is unimodal.
The successfule outcomes that fit your problem are a 3,6,9 and 12. There are 36 combinations, of which 3 can be the outcome of 2 events (1,2) and (2,1), 6 can be the outcome of 5 events, (1,5), (2,4), (3,3), (4,2), (5,1), 9 can be the outcome of 4 events (3,6),(4,5),(5,4), (6,3) and 12 is the outcome of 1 event (6,6). So out of the 36 combinations, we have 2+5+4+1 or 12 events, so 12/36 = 0.33. Now, if you throw two dice 100 times, and on the average this experiment should have 33.33 successes. Of course, some times you might have 41 successes, some times 35, but the long term average of 100 throws is 33.33 successes. This I would call the expected number of occurrences, not experimental probability. -- A bit extra to my answer: In experiments that involve chance, the results are never known. I might throw the dice 100 times and calculate a 40% of the time have success or a 25% of the time have success. These estimates are called proportions and are, I think, your "experimental probabilities" or sample estimates of success probability of your population. Of course, as given we know the success probability of the population (0.33). The binomial distribution can provide the probability of tossing two dice, "n" times and obtaining "x" successes, where the probability is 0.33. For example, I can state that 80% of the time, the number of successes will be between 27 and 39, when the dice are thrown 100 times using the binomial distribution. This is calculated by calculating the probability of 39 or fewer successes occur minus the probability of 27 or fewer sucesses occur. I have to use the cumulative distribution function (CDF). In Excel, I calculated: +binom(33-a1,100,0.33,TRUE)-binom(33-a1,100,0.33,TRUE) and varied a1 (whole numbers). When I tried a1=6, I obtained the 80%. At a1=8 (25 to 41 successes) I have the 91% confidence interval. The TRUE parameter means that I am using the CDF of the binomial distribution.
What is used to determine the probability of two indepepdent events occurring?
Multiply together the probability that each event would have of occurring by itself. For example, the probability of rolling a "3" on a single die is 1/6 ,because there are 6 different possibilities. And the probability of flipping a "heads" on a coin is 1/2 , because there are two possibilities. Then the probability of rolling a "3" AND flipping a "heads" is ; 1/6 x 1/2 = 1/12 .
What are disadvantages of sampling?
Mostly can be biased and in some cases can choose people/units innapropriate for the circumstances
What is the sample space of the word electronic?
I believe the answer is e-l-e-c-t-r-o-n-i-c there are two "c" s. You may not need to spell the word as it is usually spelled; however the letters in the word itself are the sample space. I would love to know if this is correct.
What is the probability that a 1200 hr light bulb will burn out in 1000 hrs?
There is not enough information to answer the question but if my personal experience is anything to go by, it is pretty close to 1.
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The largest factor of a light bulb not reaching its expected life expectancy is rough use or vibration. The duty cycle of the lamp also has a bearing on the longevity of the bulb, the more cycling of the lamp the shorter the life will be.
What is the probability that a family of 2 children has exactly 2 boys?
Probability equals the number of ways an event can occur divided by the total number of events. The total number of events is (b=boy, g=girl) is bb, bg, gb, gg. The probability is then 1/4.
What is the probability of tossing a coin and getting a head?
The probability of tossing a coin and getting heads is 0.5
We know that there are two possibilities for a coin to land on, heads or tails, and there are six possibilities to roll, 1 to 6, so for ever one of the possibilities for the coin there are six possibilities for the die so we do 6x2 and get 12. To prove this I will write it all out t is tails and h is heads:
T1, T2, T3, T4, T5, T6, H1, H2, H3, H4, H5, H6. If you count them you get 12.
The standard deviation is a number that tells you how scattered the data are centered about the arithmetic mean. The mean tells you nothing about the consistency of the data. The lower standard deviation dataset is less scattered and can be regarded as more consistent.
