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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 rolling a 5 and a 2?
there is a probability of 1/6.
Answer:
For two dice to show 5 and 2:
- There are two ways to roll a "good" number (2 or 5) for the first dice. This gives odds of 2/6.
- For the second dice there is one way to role a good number ( 1 in 6)
- The odds to roll both a 2 and a 5 are (2/6)x(1/6) or 2/36 or 1/18.
If you toss a fair coin 90 times how many times would you expect a heads to be face up on the toss?
Given that this is discrete data and the probability of each outcome is the same, i.e. E(P(x=1))=0.5=E(P(x=0)), and the law of large numbers says that over many trials n the outcome of a value tends to its expectation, over 90 trials you would expect around 45 of the results to be heads. That is, n=90, E(x)=0.5, 90*0.5=45.
What are four requirements for binomial distribution?
A binomial experiment is a probability experiment that satisfies the following four requirements:
1. Each trial can have only two outcomes or outcomes that can be reduced to two outcomes. These outcomes can be considered as either success or failure.
2. There must be a fixed number of trials.
3. The outcomes of each trial must be independent of each other.
4. The probability of a success must remain the same for each trial.
How many ways can you arrange abcd?
Since there are 4 letters, they can be arranged 4! ways (4*3*2*1) or 24 ways.
If you roll two fair dice once what is the probability you will obtain at least one 2 or one 5?
There are 6X6 or 36 different possibilities. Of these, 12 involve the first die being either a 2 or a 5 (as well as four results with either two 2s, two 5s or a 5 and a 2 (two of these, 5 on first 2 on second and 2 on first 5 on second)). With the 24 remaining rolls (where the first die is either 1,3,4 or 6), 2/6 will involve a 2 or a 5 on the second die. this gives us 8 new rolls in which the first die did not have a 2 or a 5 but the second did. So 12 + 8 gives us 20/36 or .555 cases where at least one of the rolls was either a 2 or a 5.
An alternate way to get here is to realize that we have a 2/6 chance for each die to get a 2 or a 5. If we add these probabilities together we would conclude that there is a 4/6 probability and that 24 of the rolls will be either a 2 or a 5 BUT we have actually double-counted the cases where they BOTH have a 2 or a 5 (remember those 4 cases) so if you subtract those 4, it will get you to 20 as well.
If you toss a coin 48 times how many times is it likely to land tails up?
There are two answers to this question. If it can only land on heads or tails up, then there is a 50% chance ( or half a chance) it will land heads up, but that's not necessarily true. But, if it can land on heads, tails, or sides, then there is a 16% chance it will land tails up.
Not sure what a mulitple choice qustion is but if it is anything like a multiple choice question, it is 1/5 or 20%.
I strongly advise you to get a dictionary, learn to spell or use a spell checker.
What is the probability that in a group of six people at least two were born in the same month?
For ease of answering, we will work under the assumption that the probability of someone being born within any given month is equal to that of any other month.
Allowing that assumption, we can look at that question a slightly different way and say "What is the probability that all people in a group of six would each be born in a different month?" The answer to that would be 12/12 * 11/12 * 10/12 * 9/12 * 8/12 * 7/12, which can also be expressed as (12! / 6!) / 126, and comes out to 665280 / 2985984, which equals 385 / 1728.
The probability of at least two being being born in the same month would then be:
1 - 385 / 1728
= 1343 / 1728
≈ 0.7772, or approximately 77.72%
representative
15 trials: 3 times
40 trials: 8 times
75 trials: 15 times
120 trials: 24 times
But don't bet on it.
How many outcomes are possible if a number cube is rolled once?
Assuming it is a 6-sided number cube, it would be 6.
What is the probability of getting two heads and one tail when a fair coin is tossed three times?
If the sequence matters (you want H-H-T in that order), then . . .
Probability of the first head = 0.5
Probability of the second head = 0.5
Probability of the tail on the 3rd toss = 0.5
Probability of the correct 3-toss sequence = (0.5 x 0.5 x 0.5) = 1/8 = 0.125 = 12.5%
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If the sequence doesn't matter, then the probability is higher.
All the possible results of 3 tosses are:
TTT
TTH
THT
THH
HTT
HTH
HHT
HHH
If the sequence doesn't matter, there are 3 different ways to get 2 heads and 1 tail.
The probability is
3/8 = 0.375 = 37.5%
Probability of the first head = 0.5
Probability of the second head = 0.5
Probability of the tail on the 3rd toss = 0.5
Probability of the correct 3-toss sequence = (0.5 x 0.5 x 0.5) = 1/8 = 0.125 = 12.5%
What is the probability of getting either a sum of 6 or atleast one 6 in the roll of pair of dice?
Each cube can fall in 6 different ways.
Two cubes can fall in (6 x 6) = 36 ways.
16 different successes:
1, 5
2, 4
3, 3
4, 2
5, 1
1, 6
2, 6
3, 6
4, 6
5, 6
6, 6
6, 1
6, 2
6, 3
6, 4
6, 5
Probability of success = 16/36 = 44.4%(rounded)
In research how to define standard deviation?
Standard deviation shows how much variation there is from the "average" (mean). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
How are the odd numbers arranged in Pascal's Triangle?
how are the odd numbers arranged Pascal's Triangle?
