Terminology
What do we call a result that could happen in a probability experiment?
Outcome
List the sample space for tossing a coin.
SS = {Heads, Tails}
What is the probability of rolling a 6 on a fair six-sided die?
Pr(rolling a 6) = 1/6
If the probability of rain is 0.3, what is the probability that it does not rain?
Pr(no rain) = 0.7
A bag contains 3 red balls and 2 blue balls. How many balls are in the bag?
5 balls
What do we call the set of all possible outcomes?
Sample Space
A spinner has the colours red, blue, green and yellow. Write the sample space.
SS = {red, blue, green, yellow}
What is the probability of rolling an even number on a fair six-sided die?
Pr(rolling an event number) = 3/6 = 1/2
The probability of winning a game is 0.25. What is the probability of not winning?
Pr(not winning) = 0.75
A coin is flipped twice. How many possible outcomes are there? List the outcomes.
4 outcomes: HH, HT, TH, TT
What is a favourable outcome?
An outcome that meets the event we are interested in.
A die is rolled. Write the sample space for rolling a number greater than 4.
ss = {5, 6}
A bag contains 4 red, 3 blue and 3 green counters. What is the probability of selecting a blue counter?
Pr(blue) = 3/10
A student has a 65% chance of completing their homework. What is the probability they do not complete it?
Pr(not completing homework) = 35%
A spinner has 8 equal sections: 3 red, 2 blue and 3 yellow. What is the probability of landing on red or yellow?
Pr(red or yellow) = 6/8 = 3/4
What does Pr(A) mean?
The probability of event A occurring.
A student chooses one ice-cream flavour and one topping.
Ice-cream flavours: Chocolate, Vanilla, Strawberry
Toppings: Sprinkles, Chocolate Chips
How many possible outcomes are in the sample space?
Ss = { (Chocolate, Sprinkles), (Chocolate, Chocolate Chips), (Vanilla, Sprinkles), (Vanilla, Chocolate Chips), (Strawberry, Sprinkles), (Strawberry, Chocolate Chips) }
There are 6 possible outcomes.
A box contains 5 red, 4 blue and 1 green marble. What is the probability of selecting red or green?
Pr(red or green) = 6/10 = 3/5
The probability that a bus arrives on time is 0.82. What is the probability it does not arrive on time?
Pr(arriving late) = 0.18
A game uses a six-sided die. You win if you roll an even number or a number greater than 4. What is the probability of winning?
SS = {2,4,6,5}
Pr(even number or greater than four) = 4/6 = 2/3
Explain the difference between an outcome, event and sample space.
An outcome is one possible result; an event is one or more outcomes of interest; the sample space contains all possible outcomes.
A spinner has 4 equal sections labelled 1, 2, 3 and 4. The spinner is spun twice. List the complete sample space and state how many possible outcomes there are.
SS =
{(1,1), (1,2), (1,3), (1,4),
(2,1), (2,2), (2,3), (2,4),
(3,1), (3,2), (3,3), (3,4),
(4,1), (4,2), (4,3), (4,4) }
There are 16 possible outcomes.
A class survey shows that 18 out of 30 students prefer dogs, while the rest prefer cats.
If one student is chosen at random, what is the probability that they prefer cats?
Pr(prefer cats) = 2/5
Students who prefer cats: 30 − 18 = 12
Pr(Cats) = 12/30 = 2/5
The probability that a student passes a test is 0.85.
What is the probability that a student does not pass the test?
Give your answer as a decimal and a percentage.
Pr(does not pass) = 1−0.85 = 0.15 or 15%
A bag contains a number of marbles coloured blue, yellow, green and red.
You have a 1/4 chance of selecting a blue marble, a 1/5 chance of selecting green and a 3/5 chance of not selecting yellow.
What is the smallest number of marbles that could be in the bag?
There are at least 20 marbles in the bag, as this is the denominator when the fractions are in their simplest forms.
Find the least common multiple of the denominators of the fractions that represent the probabilities of each colour. (4x5 = 20)
Pr(Blue) = 1/4
Pr(Green) = 1/5
Pr(Yellow) = 1 - 3/5 = 2/5
Pr(Red) = ?
1/4 + 1/5 + Pr(Red) = 3/5
Pr(Red) = 3/5 - 1/5 - 1/4
Pr(Red) = 2/5 - 1/4
Pr(Red) = 8/20 - 5/20
P(Red) = 3/20
Therefore:
P(blue) = 1/4 = 5/20
P(green) = 1/5 = 4/20
P(yellow) = 2/5 = 8/20