Probability

You are given that there is a two stage process and the first stage has four possible outcomes which are values of x and they each have probabilities that are unknown. You are given that the probability of success in part two given X = x in part one is k/x where k is a constant. You are given that the intersection of success in part two and X=x is constant for all values of x. How do you work out the probability distribution?

Probability of success given X= x equals the intersection /p(X=x) so k/x = something which is constant/P(X=x) so k/x = V/P(X=x) now what i did was I did the sum of all of them so the sum of k/x = the sum of V/p(X=x). and the sum of k/x is k/1 because the probabilites of all the outcomes of the first part is 1 so k = the V/sum of all x values so then i got k in terms of V and then i subbed that into the equation and cancelled the V so i got 250//x = /P(X=x) and then you just sub in the values of x

How to give a probability distribution (2023)

just list it seems!

How to find the probability of the first success being after m trials from a binomial distribution of success of the successes in n trials

(probability of failure)^(n-1)(probability of success)Given a normal model, sample where n have (X > a) and m have no data, what is the probability that none of the sample will have (X < b)

Given a normal model, sample where n have (X > a) and m have no data, what is the probability that none of the sample will have (X < b)

(1 - P(a<X<b)/P(x>a))to the power n x P(X>b)to the power m

Accuracy for probabilities (awrt)

3 s.f.

how to show that events are NOT independent

P(A)xP(B) = a DOES NOT EQUAL P(A intersection B) = b

How to find the probability {that an individual that has the feature x such that ( a < x < b )} is greater than q

P( q < x < b)/ P( a < x < b )

when you have information for a Venn diagram but you are only given information for two events and there may be more, but A has prob p and p is not 0 and B has prob 3P(a) then “find the possible values of P(B)'“

if no other events then 4p = 1 so

0<P(B)≤0.25

If you have the P(C|D) = 3P(C) explain whether or not C and D could be independent events

If independent P(C | D) = P(C) so C and D not

independent

If you have a binomial expansion of (p + (1-p))ⁿ what does each term represent?

The probability of r sucesses in n trials with the distribution B(n,p)

If you have a binomial expansion of (p + (1-p))ⁿ and if you have the terms with p^r and p^r+1 and you have the ratio of p^r+1/p^r “find the values of r for which p^r+1>=p^r

set the ratio as less than or equal to 1 and rearrange. DO NOT ROUND

If you have a binomial expansion of (p + (1-p))ⁿ and if you have the terms with p^r and p^r+1 and you have the ratio of p^r+1/p^r “find the values of r for which p^r+1>=p^r and you have found r is less than or equal to A what is it expected number of sucesses in n trials?

Its either the integar above or below A. because it is first integar such that the value or T before it would be less than it and the value of T after would be LESS than it. It could be either so you sub in each possible R into the fraction ratio and if its greater than 1 then it is that r, if less than 1 then its the other r