Sample Spaces
List the sample space for flipping a coin once.
{Head, Tails} S=2
A dice is rolled 12 times. The number 3 appears 4 times. What is the experimental probability of rolling a 3?
4/12 or 1/3
What is the probability of rolling a 5 on a dice?
1/6 ≈ 0.167
A dice is rolled once. Predict the chance of rolling a number less than 4.
3/6 = 1/2
What is the only even prime number?
2
List the sample space for rolling a standard dice.
{1,2,3,4,5,6} S=6
In 20 coin flips, heads appeared 9 times. What is the experimental probability of heads?
9/20 = 0.45 (45%)
What is the probability of rolling an odd number on a dice?
3/6 = 1/2
If a dice is rolled 60 times, how many sixes would you expect?
60 × (1/6) = 10
What number do you get if you multiply all the numbers on a standard dice together?
720 (1 × 2 × 3 × 4 × 5 × 6)
What is the sample space for spinning a spinner with red, blue and yellow?
{Red, Blue, Yellow} S=3
A spinner lands on blue 15 times out of 50 spins. What is the experimental probability of blue?
15/50 = 0.3 (30%)
A spinner has 4 equal sections: red, blue, green, yellow. What is the probability of landing on red or blue?
2/4 = 1/2
A spinner with 3 equal colours is spun 90 times. Predict how many times each colour will appear.
90 ÷ 3 = 30 times each
What does the Roman numeral “C” stand for?
100
Write the sample space for rolling two dice?
{(1,1), (1,2)…(6,6)} S=36 outcomes total
A student rolls a dice 30 times and gets an even number 18 times. Compare the experimental probability to the theoretical probability of rolling an even number.
Experimental = 18/30 = 0.6; Theoretical = 3/6 = 0.5; They are close but not exactly the same.
A spinner is divided into unequal sections. How can you show the probability of each outcome?
By measuring the fraction of the spinner each colour takes up (e.g., 90° out of 360° = 1/4).
A coin is tossed 100 times. Predict the number of tails.
100 × (1/2) = 50
How many sides does a dodecagon have?
12
A bag has 2 red, 3 green, and 1 yellow marble. What is the sample space if you pick one marble?
{Red, Red, Green, Green, Green, Yellow}
Explain why experimental probability might be different to theoretical probability.
Because of chance, small sample size, or randomness in experiments. Results get closer to theoretical with more trials.
Draw a spinner that could give: P(red)=1/2, P(blue)=1/4, P(green)=1/4.
A spinner divided into 2 equal halves (red), 1 quarter (blue), 1 quarter (green).
A spinner lands on pink 12 out of 30 times. Predict how many times it will land on pink if spun 100 times.
(12/30) × 100 = 40
What is the sum of the angles in a triangle?
180°