http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables
Find the frequency of getting 2 heads( 2 H).
The frequency is equal to 4. Therefore, for 2 coins tossed 10 times, there were 4 times that both coins landed on
heads. You can now calculate the experimental probability.
P( 2 H) =
4
10
P( 2 H) = 0 .40 or 40%Points to Consider
- How is the calculator a useful tool for calculating probabilities in discrete random variable experiments?
- How are these experimental probabilities different from what you would expect the theoretical probabilities to
be? When can the 2 types of probability possibly be equal?
Guided Practice
You are in math class. Your teacher asks what the probability is of obtaining 5 heads if you were to toss 15 coins.
a. Determine the theoretical probability for the teacher.
b. Use the TI calculator to determine the actual probability for a trial experiment of 10 trials.
Answer:
a. Let’s calculate the theoretical probability of getting 5 heads in the 15 tosses. In order to do this type of calculation,
let’s bring back the factorial function from an earlier concept.
Numerator (Top)
In the example, you want to have 5 H’s and 10 T’s. Our favorable outcomes would be HHHHHTTTTTTTTTT, with
the H’s and T’s coming in any order. The number of favorable outcomes would be:
number of favorable outcomes=
number of tosses!
number of heads!×number of tails!
number of favorable outcomes=15!
5!×10!
number of favorable outcomes=15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
( 5 × 4 × 3 × 2 × 1 )×( 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 )
number of favorable outcomes=1. 31 × 1012
120 × 3628800
number of favorable outcomes= 3003