http://www.ck12.org Chapter 4. Probability Distributions
Example B
Owen flips a coin 3 times. Find the probability of flipping exactly 0, 1, 2 and 3 heads.
First, verify that this is a binomial experiment. Each coin flip is heads or not heads. The probability of getting heads
is always 50%. The probability of getting heads is not impacted by the previous coin flip.
Second, calculate the probability for each of the four cases.
There are 3 trials so n=3. A success is getting a heads, so a is the number of heads. We will have to use the formula
four times with a=0, a=1, a=2 and a=3 to calculate all the different probabilities. The probability of success is^12 so
p=^12. The probability of failure is 1−^12 =^12 soq=^12.
P(X=a) =nCa×pa×q(n−a)P(0 heads) = 3 C 0 ×(
1
2
) 0
×
(
1
2
) 3
=. 125
P(1 heads) = 3 C 1 ×(
1
2
) 1
×
(
1
2
) 2
=. 375
P(2 heads) = 3 C 2 ×(
1
2
) 2
×
(
1
2
) 1
=. 375
P(3 heads) = 3 C 3 ×(
1
2
) 3
×
(
1
2
) 0
=. 125
Notes: The probabilities add up to 1. In this case they are symmetrical like the famous bell curve known as the
normal distribution.
Example C
Mark is taking a multiple choice quiz that he did not study for. There are 10 questions on the quiz and each question
has 4 possible answer choices. What is the probability that Mark will pass the quiz with a score of 6 or better if he
guesses randomly on each question?
First, verify that this is a binomial experiment. Each question is either right or wrong. The probability of guessing
right on each question is the same at 25%. Guessing one question right does not impact guessing the next right or
wrong (the trials are independent).
Second, calculate the probability for each possible outcome.