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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
a large number of samples of size 50 were selected at random from a normal population with mean and variance.The mean and standard error of the sampling distribution of the sample mean were obtain 2500 and 4 respectivly.Find the mean and varince of the population?
No, it is not true. Probability can be used to describe some properties of the variation but not all.
How many different 3 letter permutations can be formed from the letters in the word count?
There are 5*4*3 = 60 permutations.
In which cases normal distribution is continuos and is not continuous?
The normal distribution is always continuous.
The expected value depends on the probability mass function of Z. It is the average of the possible outcomes weighted by their probabilities.
In other words if you denote the probability mass function as p(z) then:
E[Z] = p(1)*1 + p(2) * 2 + p(3) * 3 + p(4) * 4 + p(5)*5
Where E[] denoted the expected value function. Note the sum is over all possible events (Z = 1 through 5).
Note also that for p(z) to be a proper probability mass function (PMF) it must not take on negative values and the sum over its domain must be equal to 1.
Two.
∙It will be spun on a number less than 10 in 75 times if you spin it 100 times.
Explanation:
Let x be the random variable, x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
The probability for any outcome is P(x) = 1/12. It is a flat probability distribution.
The probability that when you spin the spinner the outcome is a number greater than
10 is:
P(10 ≤ x ≤ 12) = P(x = 10) + P(x = 11) + P(x = 12 ) = 3/12 = 1/4
The probability of the complement event (that the outcome is a number smaller than 10) is: P(x < 10) = 1 - 1/4 = 3/4.
So the expected number of times the spinner outcome will be a number smaller than 10 is:
P(No. outcomes x<10 in 100 spins) = 100 ∙ P(x<10) = 100 ∙ 3/4 = 75
An area of a normal probability distribution represents?
The number 1. The area of any probability distribution equals 1.
A coin is tossed twice what is the probability that it will show heads both times?
The probability is 0.25.
Look at it this way--if you toss a coin twice, there are four equally-probable outcomes:
- tails, tails
- tails, heads
- heads, tails
- heads, heads
So the probability of heads twice in a row is one in four, or 25%.
the chance of tossing heads is 1/2 (50%) The chance of tossing the next heads is 1/2 (50%) 1/2 x 1/2 = 1/4 (25%)
Suppose you roll two dice what is the probability of rolling a sum of 7?
There are 21 different combinations of two dice. Three of them total 7 (3 + 4, 2 + 5, 1 + 6), so if you have two 'fair' dice, you have a 1 in 3 chance of totalling 7.
What is a event occurs last in the Apology?
The Apology is an interpretation of the philosopher Socrates' speech by fellow philosopher Plato. At the end of the speech, Socrates dies.
Probability of rolling a 3 twice with 2 rolls on a cube?
Probability of a 3 on the first roll = 1/6
Probability of a 3 on the second roll = 1/6
Probability of both of them = (1/6) x (1/6) = 1/36 = 0.0277777 = 2.78% (rounded)
Event A has probability 0.5 event B has probability 0.6 which of the following must be true?
the probabilty of both events is true. but which is most reliable is probabilty of B as it is more near to 1( total probabilty of any event)
There are 5 digits in 24680; think of them as 5 compartments. You can select 5 numbers for the 1st compartment, 4 numbers for the 2nd compartment, 3 numbers for the 3rd compartment, 2 numbers for the 4th compartment, and 1 number for the 5th compartment. So, the answer is 5*4*3*2*1 or 5! or 120
What are the odds of rolling five ones with a dice in six tries?
You can do it in 6 ways:
11111x
1111x1
111x1x
11x111
1x1111
x11111
Each has the same probability: (1/6)5 x (5/6) = 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 5/6 = 5/46656
So the probability is 5/46656 x 6 = 5/7776
You can use the binomial theorem so answer more complex questions like these.
There are nine possible successes:
1 - 5
5 - 1
2 - 4
4 - 2
3 - 3
3 - 6
6 - 3
4 - 5
5 - 4
The probability of success = 9/36 = 0.25 = 25%
What is the number of distinguishable permutations of the group of letters in the word VILLAIN?
Permutations of 7 letters = (7 x 6 x 5 x 4 x 3 x 2 x 1)
Divide by 2 because swapping the two 'I's is indistinguishable.
Divide by 2 because swapping the two 'L's is indistinguishable.
Distinguishable permutations = (7 x 6 x 5 x 4 x 3 x 2) / 4 = 1,260
What is the probability of obtaining atleast one tail when a coin is flipped six times?
you are looking for the probability of getting one tail, two,......., and six
this equivalent to saying 1 - the probability of not getting any tails (or getting 6 heads = (1/2)^6).
P(X>=1) = 1 - (1/2)^6=
