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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 a random variable in probability theory?
Random Variable in probability theory is defined as follows: Assuming you have variables Xi where i is an integer ie: i=1,2,3.......n a variable Xi is called a random variable iff(if and only iff) and random selection yields a variable Xi for i=1,2.........,n with the same likelihood of appearance. i.e prob(X=Xi)=1/n
What is the probability that 4 randomly selected people all have different birthdays?
Let us assume that there are exactly 365 days in a year and that birthdays are uniformly randomly distributed across those days.
First, what is the probability that 2 randomly selected people have different birthdays? The second person's birthday can be any day except the first person's, so the probability is 364/365.
What is the probability that 3 people will all have different birthdays? We already know that there is a 364/365 chance that the first two will have different birthdays. The third person must have a birthday that is different from the first two: the probability of this happening is 363/365. We need to multiply the probabilities since the events are independent; the answer for 3 people is thus 364/365 × 363/365.
You should now be able to solve it for 4 people.
What is the chances of winning the lottery?
It depends on the particular lottery. For Mega Millions, which is five balls out of a field of 56, and one ball out of a field of 46, the odds of hitting the jackpot are 1 in 56 * 55 * 54 * 53 * 52 / 5 / 4 / 3 / 2 * 46 or 1 in 175,711,536. In short - slim to none.
The odds are far greater for getting in a fatal automobile accident or being struck by lightning. Gee - I should play because I have been struck by lightning!
What is the probability of giving birth to a baby girl?
You have a 1 in 2 chance of having a girl. No matter how many boys you have had in the past or how many girls you have had in the past, each pregnancy presents the opportunity to have a girl or a boy with a 50% chance. The sperm does not know that it had already produced ,say, 5 boys and needs to produce a girl for you and your partner. So with every pregnancy there is a 50% chance you will have a girl and a 50% chance you will have a boy.
What is the probability of a 28-year-old female bearing a baby with Down syndrome?
If you look at the link below, the probability of a 28 year old female having a baby with Down syndrome is a little less than 1 in 1000.
What are the chances of rolling the number seven with two dice?
There are 36 permutations of two dice. Of these, six have a sum of seven. The probability, then, of rolling a seven on two dice is 6 in 36, or 1 in 6, or about 0.1667.
It does not matter if two dice are rolled one time, or if one die is rolled two times. The probability of rolling a sum of 7 is still about 0.1667.
The first thing to do is to identify all possible combinations which could give the sum of 7. These are: 6 and 1, 5 and 2, 4 and 3, 3 and 4, 2 and 5, and 1 and 6.
Thus there are 6 possible combinations.
For each of these combinations, the probability of getting the 1st number correct is 1/6 and the probability of getting the second number correct is 1/6, and so the overall probability of the combination is 1/36
There are 6 ways to get 7 though so 6x 1/36 = 1/6
Which means the probability that 2 dice rolls will add up to 7 is 1/6
What is the probability of getting three tails if you flip a coin three times?
Since the probability of getting tails is 50% or 0.5, the probability of three tails would be 0.5*0.5*0.5=0.125 or 12.5 %
What is the probability tossing a fair coin n times?
The probability will b 0.5. since a coin tossed n times has 2n no. of desired results, among which only half that is n times it can b tail. Hence P = n/2n i.e 0.5.
What three digit number has the most factors?
Using prime factorization, there are 2 three digit numbers with 9 factors:
512 and 768.
There are no three digit numbers with 10 or more prime factors.
512=2^9 and 768=3*2^8
If the probability of a person being left handed is .11, then the probability of a person being right handed is .89 (1.00 - .11). In a class of 40 people, there are 40! (40 factorial) = 40 x 39 x 38 x .... x 3 x 2 x 1 possible Permutations of students. Within this number, there are many that will yield exactly 5 left handed people. 40-P-5 is the number of Permutations of 5 within a class of 40 (sorry, can't use the correct formating here!): = 40! / (40 - 5) ! = 40! / 35! = 40 x 39 x 38 x 37 x 36 Since we don't care about order..... we need to factor out the number of identical permutations. 40-C-5 = 40-P-5 / 5! So.... (40 x 39 x 38 x 37 x 36) / (5 x 4 x 3 x 2 x 1) = 658,008 Now, what is the probability of any one such combination? (.89 to the power 35) x (.11 to the power 5) = 0.000000273 So the probability of exactly 5 left handed people in the class is 658,008 x .000000273 = 17.9408137 %
Since Luis can only pass or fail his test, and we know that the probability of all possible outcomes is 1, we therefore see that P(Pass) + P(Fail) = 1
*where P(X) = the probability of event X*
So if P(Pass) = .33;
then P(Fail) = 1 - P(Pass)
= 1 - .33
= .66 (or 66% chance that Luis will fail)
0.205
0.894
This is the same as example 2 in the link below
Why does main sequence has a limit at the lower end?
The reason main sequence has a limit at the lower end is because of temperature and pressure. The lower limit exists in order to exclude stellar objects that are not able to sustain hydrogen fusion.
What are the chances of having a baby boy after having 3 girls?
Approximately 50% - the same as if you didn't have 3 girls previously.
What is the probability that the sum of the numbers on two dice is even when they are rolled?
It's1/12
If you flip a penny and it lands on its side what does it mean?
It means it is rare. It is possible, but happens only, like, maybe every four years or something.
the probability would be 1/3
a polygon with 6 sides
* * * * *
The fact that is has six sides makes it a hexagon but that does not explain ""convex". A convex polygon is one in which none of the angles is a reflex angle. An alternative definition of convex is that a line joining any two points inside the hexagon is wholly inside the shape.
What is the probability that at least 1 head appears in 3 tosses of a fair coin?
7/8 , 87,5% The easiest way is to turn the question around. No heads means that they are all tails and the priobability of all tails is 1/8 (everybtail 1/2 so 1/2 x 1/2 x 1/2) At least one head is therefore 1- 1/8 8/8-1/8 = 7/8 A more complicated way all 8 options are HHH,HHT,HTH, HTT, THH THT TTH TTT. (8 in total) seven do have atleast one head so 7/8. (Of course the same answer)
How many face cards are in a deck of 52 cards?
In a deck of 52 cards, there are four suits. Each suit contains an ace and the numbers two through ten as well as a Jack, Queen, and King. In a modern deck, there are twelve face cards in all.
i think since they are mutually exclusive events the probability would by 9/10*7/10 = 63/100
The chance of the child having schizophrenia when both parents have schizophrenia is about 37%. There is no data available for other combinations of illnesses, for example if one parent has schizoaffective disorder and the other has schizophrenia.
