Download Probability Review (grade 8)

Probability Review
Instructions: As we will be beginning a new unit on probability, we should review what we
learned from last year! Read the first page and attempt the review problems. If you require
further information, refer to pages 236-246 of Math 3000.
1. Probability Terms
Universal Set or Sample Space: The set of all possible outcomes. (e.g. the universal set for
rolling a dice is the set of numbers {1,2,3,4,5,6}.)
Compatible and Incompatible Events: Compatible events can both happen together and
incompatible events can never happen together. (e.g. Compatible events: raining on a
Tuesday. Incompatible events: The Maple Leafs winning the Stanley Cup and me still being
alive (joke). Incompatible events: having a vegetarian dinner and having a roast beef
sandwich for dinner.)
Complimentary Events: Events which are incompatible but together make up the sample
space. (e.g. Westmount Knights win the game and Westmount Knights lose the game.)
Dependent and Independent Events: Events which do not care about the outcome of each
other are independent (e.g. flipping a coin is not influenced by previous flips). Events which
are dependent are influenced by previous outcomes (e.g. Bingo).
2. Probability of an Event
If E is an event, P ( E ) refers to the probability of the event E happening. It is calculated by:
number of successful outcomes
.
P( E ) 
number of possible outcomes
The number of successful outcomes is simply the number of ways E can happen.
E  choosing an ace from a deck of cards
e.g.
P( E ) 
number of aces
4
1

  7.69%
number of cards 52 13
Here, the number of successes is the number of aces that can be drawn and the number of
outcomes is the total number of cards in the deck.
3. Multi-Step Probability
If E is an event describing several steps, P ( E ) is calculated by multiplying the probabilities of
each individual step.
E  flipping heads twice in a row then rolling a 4 on a die, ( E  HH 4) for short.
e.g. P( HH 4)  P( H )  P( H )  P(4)
1 1 1 1
P( HH 4)    
 4.167%
2 2 6 24
To see where the fractions come from, P ( H ) 
P(4) 
1
because there are 6 sides on a die.
6
1
because there are 2 faces to a coin and
2
Review Problems
4. a) Rolling a six on a die.
b) Rolling two dice that add to 6 (hint: make a chart).
c) Flipping a coin heads 2 times in a row.
d) Drawing a heart, replacing it, and then drawing a club.
e) Drawing a heart without replacing it and then drawing a club.
5. a) Make a tree diagram (refer to 3000 p. 246) to model the event of flipping a coin 3 times.
b) What is the probability of flipping heads 3 times?
c) What is the probability of flipping tails exactly twice?
d) Are the steps in this experiment dependent or independent? Explain.
6. BINGO has 75 numbers preceded by one of the letters B,I,N,G,O to indicate which column
the number goes in. The game is played on a 5x5 card with the centre square a “free”
square. One of the ways a game is won is by completing a line of 5. Marzia is playing and
gets I21 then B5, both of which are on her diagonal! She only needs G52 and O71 to win!
Find the probability that she wins after the next 2 turns. What is the probability she has to
keep playing?
7. The histogram to the right shows the heights of
black cherry trees. Use it to find the following
probabilities:
a) Probability of a tree being between 80 and 85 feet.
b) Probability of a tree being at least 70 feet.
c) Probability of a tree being between 65 and 85 feet.
d) What is the name for the kind of probabilities you have calculated here?
8. Mr. Brett’s math classes are doing a lottery. There are 100 tickets. 5 of the tickets are
winners. (The prizes are a top hat, Jupiter, a Nascar, some funky sunglasses and a big bag
of money.) Find the probability that the first 5 people to select tickets all win.
9. Caitlin, Sarah and Chamara are working on a project. One person has to write a report, one
has to make a poster and another has to present to the class. How many different ways can
the group divide the labour assuming each person has only one task?
10. At a fast food restaurant, the choices for sandwich are hamburger or submarine; the choices
for drink are juice, water or pop and the choices for a side are salad or fries.
a) Make a tree diagram demonstrating all the available combos.
b) Zach asks Michael to randomly order for him. What is the probability that Michael orders
him a hamburger with salad?
11. Cristina, Nikalas, Tyus, Banine, Fiona and Liam are all going to play soccer. To choose their
position for a pick up game, they reach in and randomly pull out a jersey without replacing it.
The 6 jerseys are: goalie, striker, left defense, right defense, left forward and right forward.
a) What is the probability that Cristina gets the goalie jersey?
b) What is the probability that Cristina gets the goalie jersey and Nikalas gets the striker
jersey?
c) Find the probability of the players selecting the following lineup:
LF – Cristina
Striker – Tyus
RF – Fiona
LD – Banine
G – Liam
RD – Nikalas