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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
Suppose you toss a fair coin 75 times how many times would you expect to get heads?
A fair coin means that the probability of a head = probability of a tail = 1/2
So you would expect half the tosses to be heads, ie 1/2 x 75 = 371/2 heads.
...oooOOOooo...
Having 1/2 a head doesn't seem possible, but when the question asks about expectation, it is saying: if you repeated the experiment lots of times, how often, on average, would the required result appear.
So the expectation of heads when a fair coin is tossed 75 times is asking: if a fair coin was repeatedly tossed 75 times, what would be the (mean) average number of heads achieved?
As more and more trials are done and the (mean) average of the number of heads got is taken, it will get closer and closer to 371/2
37 or 38 times. (Obviously, you can't have half of a time.) You will either get one or the other, and a fair coin means that either is just as likely. So, it should split evenly down the middle.
Gwerth Probablitiy
What is a number occurring most frequently in a set of numbers?
The mode is the value which occurs most frequently in a set of numbers.
Random Sample
1 - (2/3)4
= 1 - 16/81
= 65/81
≈ 80.25%
The odds of not selecting a queen of hearts?
The odds of not selecting a queen of hearts is 51 in 52.
4/25
This is a very simple statistic to comprehend and to calculate. It takes the frequency distribution method of calculating probability. The statistic is calculated as
This statistic is simple to interpret as well. What it calculates is the probability of the portfolio to get a negative return. It can be comprehended that a higher figure would mean a higher probability of fund to do give negative returns.
Why random sampling is important?
Random sampling is important because it is much more practical to test a small group of results than a bigger whole. Say, for instance, a company wants to test the average voltage of a battery they manufacture. It would be much more practical to test 1000 randomly chosen batteries than to test 100000.
One six-sided dice are rolled what is the probability?
Due to the incompatibility of the grammar: "one" and "are", the question makes no sense and so it is not possible to answer it.
Prob(X > 0.57) = Prob(Z > 2) = 0.02275 = 2.275%
If the dice is rolled 450 times how many times would you expect to get 4?
The probability of rolling a four on a single roll of a fair die is 1/6. So the expected number of 4s in 450 rolls is 450*1/6 = 75.
What is the probability that you will spin a 4 and roll a 4?
Assuming each possible number on a spinner has the same probability and an unbiased die is being rolled, the answer depends on how many numbers are on the spinner, and how many times the number 4 appears on each.
To find the probability, workout the probability of spinning a 4 on the spinner and the probability of rolling a 4 on the die; then as spinning the spinner has no effect on rolling the die, they are independent events and to get the probability of both happening multiply them together.
The probability of success is the number of successful outcomes divided by the total number of outcomes, giving:
Probability(spinning a 4) = how_many_4s_are_on_the_spinner / how_many_numbers_are_on_the_spinner
Probability(rolling a 4) = how_many_4s_are_on_the_die / how_many_numbers_are_on_the_die
Probability(spinning a 4 and rolling a 4) = Probability(spinning a 4) × Probability(rolling a 4)
Examples:
- an octagonal spinner with the numbers 1-4 on it each twice and a tetrahedral die (as used in D&D games) with the numbers 1-4 on it→ pr(spin 4 & roll 4) = 2/8 × 1/4 = 1/16
- a decagonal spinner with the numbers 0-9 and a tetrahedral die with the numbers 0-3 on it→ pr(spin 4 & roll 4) = 1/10 × 0/4 = 0
- a decagonal spinner with the numbers 0-9 and a standard die with the numbers 1-6 on it→ pr(spin 4 & roll 4) = 1/10 × 1/6 =1/60
What is the probability of getting two tails and one heads if a coin is tossed three times?
Out of the 8 possible combinations, three are favorable: HTT, THT, TTH. Therefore, the answer is 3/8.
Out of the 8 possible combinations, three are favorable: HTT, THT, TTH. Therefore, the answer is 3/8.
Out of the 8 possible combinations, three are favorable: HTT, THT, TTH. Therefore, the answer is 3/8.
Out of the 8 possible combinations, three are favorable: HTT, THT, TTH. Therefore, the answer is 3/8.
4+4+5=12 so you figure this out by 12! which is 12x11x10x9x8x7x6x5x4x3x2 and then divide by 4! 4! 5! and you get you answer(:
Why are the results for theoretical and experimental probability different?
The theoretical model does not accurately reflect the experiment.
The probability that two dice rolled will each have the same value is 1 in 6.
Independence of the two samples means that the choosing of the first sample did not influence the choosing of the other sample, and vice versa.
For example, if you were comparing running speed in two different brands of running shoes, you could look at two samples of people running a 100 m dash -- one sample of people running in Brand A and one sample of people running in Brand B. If those two groups were picked independently of one another, these samples would be independent. If, instead, you had the same group of people run the race twice (once in each brand of shoe), these samples would be dependent.
Samples that are not independent are said to be "correlated", "interdependent", or "dependent". Because the two samples are correlated, you might get incorrect findings for your statistical study. For example, say you want to compare the heights of boys and girls. If you chose the samples by choosing a girl for the girl sample, then choosing her brother for the boy sample, your statistical analyses might be misleading if you didn't account for the fact that tall girls are more likely to have tall brothers, and short girls are more likely to have short brothers. By choosing siblings for the two groups, you have made the two samples not independent of one another.
If the independence assumption is violated, you have to do a special type of statistical test. For example, instead of doing a two-sample t-test, you would have to do a paired t-test.
