CK-12 Basic Probability and Statistics - A Short Course

http://www.ck12.org Chapter 3. Discrete Random Variables - Basic

Now let’s go back to our original chapter problem and see if we have gained enough knowledge to answer it.

You are in statistics class. Your teacher asks what the probability is of obtaining five heads if you were to toss 14
coins.

(a) Determine the theoretical probability for the teacher.

(b) Use the TI calculator to determine the actual probability for a trial experiment for 20 trials.

Solution:

(a) Let’s calculate the theoretical probability of getting 5 heads for the 14 tosses.

Numerator (Top)

In our example, we want to have 5 H and 9 Ts. Our favorable outcomes would be any combination of HHHH-
HTTTTTTTTT. The number of favorable choices would be:

#o f favorable choices=

#possible letters in combination!

letter X!×letter Y!

#o f favorable choices=

14 letters!

5 head!× 9 tails!

#o f favorable choices=

14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

( 5 × 4 × 3 × 2 × 1 )×( 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 )

#o f favorable choices=

8. 72 × 1010

( 120 )×( 362880 )

#o f favorable choices=

8. 72 × 1010

( 43545600 )

#o f favorable choices= 2002

Denominator (Bottom)

The number of possible outcomes= 214

The number of possible outcomes= 16384

Now we just divide the numerator by the denominator.

P( 5 heads) =

2002

16384

P( 5 heads) = 0. 1222

The probability would be 12% of the tosses would have 5 heads.

b)