Grade 7 Mathematics
PROBABILITY measures how likely something is to happen. It's a number between 0 and 1 (or 0% and 100%).
0 = Impossible | 0.5 = Equally Likely | 1 = Certain
P(event) = Number of favorable outcomes / Total number of possible outcomes
Can be written as a fraction, decimal, or percent!
Sample Space: The set of ALL possible outcomes of an experiment
Theoretical Probability: What SHOULD happen based on math
Experimental Probability: What ACTUALLY happens when you try it
Favorable Outcome: The outcome you're looking for
Rolling a standard die:
1 2 3 4 5 6
Sample Space = {1, 2, 3, 4, 5, 6} = 6 outcomes
P(rolling a 4) = ?
Favorable outcomes: 1 (just the 4)
Total outcomes: 6
P(4) = 1/6 = 0.167 = 16.7%
P(rolling an even number) = ?
Favorable outcomes: 3 (the numbers 2, 4, 6)
Total outcomes: 6
P(even) = 3/6 = 1/2 = 0.5 = 50%
P(rolling a number less than 5) = ?
Favorable outcomes: 4 (the numbers 1, 2, 3, 4)
Total outcomes: 6
P(less than 5) = 4/6 = 2/3 = 0.667 = 66.7%
A bag contains:
5 red marbles | 3 blue marbles | 2 green marbles
Total = 5 + 3 + 2 = 10 marbles
Find these probabilities:
P(red) = 5/10 = 1/2 = 0.5 = 50%
P(blue) = 3/10 = 0.3 = 30%
P(green) = 2/10 = 1/5 = 0.2 = 20%
P(NOT green) = 8/10 = 4/5 = 0.8 = 80%
Match these events to the scale:
P = 0: Rolling a 7 on a standard die (impossible)
P = 0.17: Rolling a specific number (1/6)
P = 0.5: Flipping heads on a coin
P = 0.83: Rolling a number OTHER than 6
P = 1: Rolling a number 1-6 (certain)
WRONG: Getting a probability greater than 1 or less than 0.
RIGHT: If your answer is greater than 1 (or 100%), you made an error! Check that favorable outcomes don't exceed total outcomes. Probability is ALWAYS 0 to 1.
1. A spinner has 8 equal sections: 4 red, 2 blue, 1 green, 1 yellow.
a) Sample space size: outcomes
b) P(red) =
c) P(blue or green) =
d) P(NOT yellow) =
2. A deck has 52 cards: 13 hearts, 13 diamonds, 13 clubs, 13 spades. Hearts and diamonds are red; clubs and spades are black.
a) P(heart) =
b) P(red card) =
c) P(not a spade) =
3. Is each event impossible, unlikely, equally likely, likely, or certain?
a) P = 0.9: ________________________
b) P = 0: ________________________
c) P = 1/2: ________________________
d) P = 0.15: ________________________
4. A bag has 6 red, 4 blue, and 5 white marbles. Which is MORE likely: picking red OR picking blue? Show your work.
P(red) =
P(blue) =
More likely: ________________________