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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 drawing either a 3 or a heart from a regular bridge deck of cards?
The probability of A is denoted P(A) and the probability of B is denoted P(B). P(A or B) = P(A) + P(B) - P(A and B). Say P(A) = Probability of drawing a heart, which is 13/52. Say P(B) = Probability of drawing a three, which is 4/52. We now have to determine P(A and B) which is the probability of a heart and a three, which is 1/52. We now can determine the probability of drawing a heart or a three which is 13/52 + 4/52 - 1/52 = 16/52 = 4/13.
Two dices are thrown simultaneously what is the probability that both the dices have even number?
The sample space is 62 or 36. Take the 1st die rolled. It must start with a 2, 4, or 6. Likewise, the 2nd die rolled must be a 2, 4, or 6. So, with the 1st die at 2, the 2nd die could be 2, 4, or 6. The same holds true for the 4 & 6. There are 9 possible rolls then that are even & even. The probability is 9/36 or 1/4.
2/5
If the probabilty that an event will happen is 3 what is the probability of the event complement?
The probability of event X is 0.3. If events X and Y are complements, what is the probability of event Y?
What happens to the confidence interval as the standard deviation of a distribution increases?
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
What symbol is used for probability of success in statistics?
A "p" is used for probability of success. A "q" is used for probability of failure.
The sum of the number is even when two dice rolled?
One way to do this is to list all the possible outcomes. You can get an even sum with two even numbers or two odd numbers. So here is the list.
(1,1) (3,1)
(5,1) (2,2)
(4,2) (6,2)
(1,3) (3,3)
(5,3) (2,4)
(4,4) (6,4)
(1,5) (3,5)
(5,5) (2,6)
(4,6) (6,6)
That is 18/36 so half the time the sum will be even. Second method to calculate the probability:
Also, note that to obtain an odd sum, we need and odd number one one die and an even number on the other one. So let's use that and figure out the answer another way.
The chance of even on the first is 1/2 and odd on the second is 1/2 so the chance of even and then odd is 1/4. Now, we can also have odd on the first roll then even. That chance is also 1/4. We add these two to get 1/2 which is what we found from enumeration of the possible outcomes. This is a good example of when to add and when to multiply probabilities. When we want both and odd and an even roll, we multiply because we want two events to occur at the same time and the probability of that is less than either one by itself. This is the multiplication principle.
However, when we want to look at the probability of EITHER and odd roll followed by an even or and even followed by an odd, we must ADD. Clearly these two outcomes can not occur at the same time since the first roll must be odd or even and can't be both. This tells us the chance of an odd sum is 1/2 which means the chance of an even sum is 1-1/2 or 1/2 also. Method three:
To obtain an even sum we need either two evens or two odds. Using the logic above in method 2, we see the probability of two evens is 1/4 and of two odd is 1/4. So the probability of either one of these is 1/4+1/4=1/2
What is the probability of rolling doubles greater than three?
In the case of dice, greater than three, means 4,5 or 6. So, obviously, three cases out of 36.
0.5, 1/2, 50% The probability for heads versus tails does not change based on the amount of times the coin is tossed. It will always be a 50% chance.
What is the theoretical probability of drawing a joker out of a deck of cards?
If there is only one joker, the odds are 1 in 53. If there are two jokers the odds are 1 in 27.
About a 3.8% chance (2 / 52 = 0.038...).
How many different four-letter initials are there that begin with A?
26^3. There are 26 possible letters, so that is why we multipy by 26. Because there are 4 positions, and the first is taken with "A", that only leaves 3 positions left. As there are 26 possible letters in each position, you multiply by 26 three times, or, 26 to the third power.
If you roll a die what is the probability that a three will appear on top?
I think it's 1 out of 6 chance.
Why is the probability measured as a number between zero and one?
Probability is the ratio of no. of possible outcomes to the maximum no. of outcomes .
If any event doesnt occurs ,then it is 0/N,where N=maximum no of outcomes .and that is 0 itself ,hence that is signified by zero ,or will at max, all the possible outcomes wil occur ,which means N/N that is denoted by 1.
Hence probabilty for the occurance for any event is between 0 and 1.
If you toss a number cube 600 times what is the most probable number of times you will get a 3?
100/600 or 1/6
If 20 newborn babies are randomly selected how many different gender sequences are possible?
You have 2 choices for 20 times, so the number of sequences is 220 or 1048576.
Relative frequency approximation is conducting experiments and counting the number of times the event occurs divided by the total number of events. The classical approach is determine the number of ways the event can occur divided by the total number of events.
What is the possible outcome of flipping a coin?
Each time you flip a fair coin it has the same equal chance of landing on heads or tails. That is, even if you get (for example) 19 heads in a row, the next flip still has 50% chance of landing on tails (if the coin is fair).
What is the difference between standard error of sample mean and sample standard deviation?
Standard error
A statistical measure of the dispersion of a set of values. The standard error provides an estimation of the extent to which the mean of a given set of scores drawn from a sample differs from the true mean score of the whole population. It should be applied only to interval-level measures.
Standard deviation
A measure of the dispersion of a set of data from its mean. The more spread apart the data is, the higher the deviation,is defined as follows:
Standard error x sqrt(n) = Standard deviation
Which means that Std Dev is bigger than Std err
Also, Std Dev refers to a bigger sample, while Std err refers to a smaller sample
Why must scientists use the concept of probability for the structure of an atom?
This is due to Heisenberg's principal of uncertainty.
The 68-95-99.7 rule states that in a normally distributed set of data, approximately 68% of all observations lie within one standard deviation either side of the mean, 95% lie within two standard deviations and 99.7% lie within three standard deviations.
Or looking at it cumulatively:
0.15% of the data lie below the mean minus three standard deviations
2.5% of the data lie below the mean minus two standard deviations
16% of the data lie below the mean minus one standard deviation
50 % of the data lie below the mean
84 % of the data lie below the mean plus one standard deviation
97.5% of the data lie below the mean plus two standard deviations
99.85% of the data lie below the mean plus three standard deviations
A normally distributed set of data with mean 100 and standard deviation of 20 means that a score of 140 lies two standard deviations above the mean. Hence approximately 97.5% of all observations are less than 140.
.30*200*15= 900
.50*320*30= 4,800
.20*410*40= 3,280
Total= 8,980
