http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables
The randomness of an individual outcome occurs when we take 1 event and repeat it over and over again. One
example is if you were to flip a coin multiple times. In order to calculate the probability of this type of event, we
need to look at one more formula.
The probability of gettingXsuccesses inntrials is given by:
P(X=a) =nCa×pa×q(n−a)where:
ais the number of successes from the trials.
pis the probability of the event occurring.qis the probability of the event not occurring.
Now, remember that in previous Concepts, you learned about the formula fornCr. The formula is shown below:
nCr=n!
r!(n−r)!Also, recall that the symbol!means factorial. As a review, thefactorial function (!)just means to multiply a series
of consecutive descending natural numbers.
Examples:
4!= 4 × 3 × 2 × 1 = 24
6!= 6 × 5 × 4 × 3 × 2 × 1 = 720
1!= 1
Note: it is generally agreed that 0!=1.
Technology Tip: You can find the factorial function using:
MATH I I I (PRB)H H H ( 4 )
Interestingly, it was Blaise Pascal (pictured below) with Pierre de Fermat who provided the world with the basics
of probability. These 2 mathematicians studied many different theories in mathematics, one of which was odds and
probability. To learn more about Pascal, go to http://en.wikipedia.org/wiki/Blaise_Pascal. To learn more about
Fermat, go to http://en.wikipedia.org/wiki/Fermat. These 2 mathematicians have contributed greatly to the world
of mathematics.