Dear Experts:

I have what I think are a couple of basic probability questions that I can't get my head around. I don't know anything about statistics, so bear with me.

Here's my question: assume that are four independent, uncorrelated events, each of which has a 25% chance of occurring. Three questions:

1) What is the chance that any one of the four events will occur? In other words, there are four 25% chances--is there thus a 100% probability of one of the events occuring?

2) What is the probability that any two of the four events will occur?

3) Is the probability that all four events will occur equal to (.25 x .25 x .25 x .25)?

Please excuse if I am using improper or inexact terminology. Please include the basic formula with any answer...

Regards,

TMR

1) What is the chance that any one of the four events will occur? In other words, there are four 25% chances--is there thus a 100% probability of one of the events occuring?

This is the chance of

A happening and not B, C or D

+

B happening and not A, C or D

+

C happening and not A, B or D

+

D happening and not A, B or C

This is

(0.25*0.75*0.75*0.75)+(0.2

=0.421875

2) What is the probability that any two of the four events will occur?

There are 6 way that exactly 2 events will occur:

ABCD

------

0011

0101

0110

1001

1010

1100

=(0.75*0.75*0.25*0.25)*6

=0.21093756

3) Is the probability that all four events will occur equal to (.25 x .25 x .25 x .25)?

Yes you care correct