In a survey conducted by helena, a financial consultant, it was revealed of her 426 clients
288 own stocks.
200 own bonds.
184 own mutual funds.
123 own both stocks and bonds.
106 own both stocks and mutual funds.
102 own both bonds and mutual funds.
how many of helena's clients own stocks, bonds, and mutual funds? (assume each client invested in at least one of the three types of funds.)

There are 85 Helena's client own stocks, bonds and mutual funds.

Step-by-step explanation:

Since we have given that

Let A: who own stocks

B : who own bonds

C : who own mutual fund

So, According to question,

n(A) = 288

n(B) = 200

n(C) = 184

n(A∩B) = 123

n(B∩C) = 106

n( A∩C) = 102

n(A∪B∪C) = 426

As we know the formula :

Hence, there are 85 Helena's client own stocks, bonds and mutual funds.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

true? is that what you're asking or do you mean something else?