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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
hypergeometric distribution f(k;N,n,m) = f(1;51,3,1)
or binominal distribution f(k;n,p) = f(1;1,3/51) would result in same probability
This question does not have a unique answer unless we make an additional assumption: we must know something about the relationship between the trials. For example, if we are monitoring a lightbulb for failure and the "event" consists of a working lightbulb, then the event not occurring means the lightbulb doesn't work. Let the "trials" consist of turning on the lightbulb. If the bulb fails on the first trial (chance of 1 - 3/8 = 5/8) then obviously it will not work on the second trial, either. The answer in this case would be 5/8 = 62.5%. If we assume the two trials are statistically independent, we are really saying we don't want to worry about these issues. Equivalently, the person asking the question is just telling us to multiply the probabilities (which means they are probably a teacher or a textbook and they or it are mainly concerned about your ability to multiply fractions, not about your understanding of probability). The chances of the event not occurring in each trial are 5/8. Multiplying gives 25/64 = about 39%. This is quite a bit less than 62.5%.
You toss a coin 5 times and it lands on heads What will it land on the 6th time?
there is a 1/2 chance that it will land on heads and 1/2 chance it will land on tails. it dosent matter what the stats are
The probability is 0.0035
How many possible outcomes are there when you roll two number cubes and toss one coin?
There are 6*6*2 = 72 possible outcomes.
There are 4 queens in 52 cards so the odds of picking a queen in one draw if 4/52. Now once you have picked a queen, there are 3 queens left and 51 cards. So 4/52 x 3/51 = 1/221 = 0.45 %
20, 40, 60, 80, or 100.
The probability is 0.2503
It is 1 - prob(none of the four is a heart)
= 1 - (39/52)*(38/51)*(37/50)*(36/49)
= 1 - 1974024/6497400 = 0.6962
We'd like to know the likelihood that any 5 people chosen from 20 will be left-handed if the probability of being left-handed is assumed to be 10%. Well, 5 people can be chosen from 20 in (20 C 5) = 15504 ways. So, we have (15504)*(.1^5)*(.9^15) = 3.19%. This is a Binomial probability problem, where we are interested in 'k' successes (k = 5, success --> people being left-handed) in 'n' trials (n = 20).
Is the Poisson probability distribution discrete or continuous?
The Poisson distribution is discrete.
The probability that a standard normal random variable Z is less than 50 is approximately 0?
False. It is approximately 1. Theoretically, it is not 1. I used excel, and I know the probability is between 0.999999 and 1. as the probability of Z<6 is 0.999999. I can't calculate the probability exactly because excel only goes to 7 place accuracy.
It should be a 16% chance. If she makes 2 out of 5 free throws, that's a 40% chance she'll make a free throw. The probability that she makes two in a row is therefore .4 * .4 = .16, or 16%.
P( a student getting an A) = 5/20=1/4
There are 3 students. The probability that all three got an A is (1/4)(1/4)(1/4)=1/64.
hypergeometric distribution f(k;N,n,m) = f(3;52,4,3)
What are the possible outcomes of tossing a coin 5 times?
There are 32 possible outcomes.
HHHHH,
HHHHT, HHHTH, HHTHH, HTHHH, THHHH,
HHHTT, HHTHT, HHTTH, HTHHT, HTHTH, HTTHH, THHHT, THHTH, THTHH, TTHHH,
HHTTT, HTHTT, HTTHT, HTTTH, THHTT, THTHT, THTTH, TTHHT, TTHTH, TTTHH,
HTTTT, THTTT, TTHTT, TTTHT, TTTTH,
TTTTT.
There is no simple answer.
First of all, the probability of boys is 0.517 not0.5.
Second, the probabilities are not independent.
If you choose to ignore these important facts, then the answer is 2/3.
50%
If you pick only one marble from the bag, at random, it can be any one of 26 marbles. Out of these, 5 of the marbles are green. Thus, there are 26 possible outcomes out of which 5 are favourable - to the event that the marble is green. Therefore the probability of a green marble is 5/26.
The calculations become more complicated if you consider choosing a green marble in several attempt: it depends on whether or not the marbles are replaced before the next one is picked.
What is the probability of getting a total of at least 9 in a single throw of two dice?
10/36. One of the easier ways to find an answer is simply to make a table showing the possibilities of every move.
1 2 3 4 5 6
1| 2 3 4 5 6 7
2| 3 4 5 6 7 8
3| 4 5 6 7 8 9
4| 5 6 7 8 9 10
5| 6 7 8 9 10 11
6| 7 8 9 10 11 12
Based on the table, there are 36 different roll combinations, with a total of 10 combinations that are at lest 9.
