Probability Distribution Binomial Distribution Geometric Distribution ...

Name: _______________________ Date: _____________ May 2012
KNOW COMM APPL THINK TOTAL
5 10 17 8 40
Probability Distribution Binomial Distribution
Expected Value : E(X)=
n
i=
1
P(x) =
−
Cpq
n x
∑ xiPx ( i)
E(X) = np
x n x
Geometric Distribution HyperGeometric Distribution
Px =
C × C
nCr E(X) = q/p
ra
Expected Value: E( X)
=
n
P(x) = q x a x n−a r−x p Probability: ( )
PART A: KNOWLEDGE
1. What is the expected value for a binomial distribution with p = 0.2 and
n = 6? (1 mark)
2. NBA basketball player Dwayne Wade scores on 92% of his free throws.
What is the expected waiting time before he misses on a free throw?
(2 marks)
3. What is the expected number of women on a six-member jury randomly
chosen from 10 women and 14 men? (2 marks)

Name: _______________________ Date: _____________ May 2012
PART B: COMMUNICATION
4. In a family with four children, determine the probability distribution
for the number of boys. (4 marks)
X Rough Work P(X)
0
1
2
3
4
5. Graph the probability distribution for the question above. (4 marks)
6. What is the expected number of boys? (2 marks)

Name: _______________________ Date: _____________ May 2012
PART C: APPLICATION
7. Mr. Neave didn’t study enough for his Finite Math exam and is
struggling on the 10 question multiple choice portion. Each question
has four possible answers. Mr. Neave is certain of four answers but
has no idea on the remaining six questions. If Mr. Neave randomly
guesses on the six questions what is the probability that he gets at
least 5 out of 10 on the multiple choice portion. (4 marks)
8. At a pet shop, an aquarium contains nine piranha and six baby sharks.
Kevin randomly selects 5 fish for his new aquarium.
a. Find the probability that Kevin gets exactly 2 sharks. (3 marks)
b. Calculate the expected number of piranha. Show your work.
(2 marks)

Name: _______________________ Date: _____________ May 2012
9. Mr. Neave will play in the Staff vs. Student Softball game. He is a
0.550 hitter. That means his probability of getting a hit is 0.55.
(a) What is the probability that Mr. Neave gets his first hit in his third
at bat? (2 marks)
(b) On which at bat would you expect him to get his first hit? (2 marks)
10. Mathex, a new medication to cure math anxiety, is effective for 75%
of the participants in clinical trials. A group of twenty patients take
this new medication.
a) What is the probability that the medication will be effective for
exactly 10 patients? Show your work. (2 marks)
b) What is the expected number of patients the drug will be effective
for? Show your work. (2 marks)

Name: _______________________ Date: _____________ May 2012
PART D: THINKING
11. Consider a simple game in which you roll a 12-sided die. If the number
you roll is prime, you win twice that amount and if the number is not
prime, you lose that amount.
c. Find the probability distribution of winnings for the game.
(3 marks)
d. Is this a fair game? Use calculations to support your answer.
(3 marks)

Name: _______________________ Date: _____________ May 2012
12. Josh Clemente is a 70% free throw shooter. His probability of
success is 0.70.
a) What is the probability that Josh will make two free throws in a row?
(1 mark)
b) What is the probability that Josh will miss two free throws in a row?
(1 mark)