A focused Grade 6 learning session for Introduction to Probability using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving introduction to probability.
Introduction to Probability means choosing a model, naming what each number means, and explaining the strategy.
Question: The spinner above is spun. Which probability is impossible?
Why it works: The spinner has only red, blue, yellow, and green sections. Purple is impossible because it does not appear on the spinner.
Answer: Purple is not on the spinner
Question: The spinner above has four equal sections. What is the probability of spinning orange or cyan?
Answer: \(\frac{1}{2}\) or \(50\%\)
Question: A square is chosen at random from the grid. What is the probability that it is pink?
Answer: \(\frac{1}{2}\) or \(50\%\)
Question: A bag contains \(3\) red marbles, \(5\) blue marbles, and \(2\) green marbles. If one marble is drawn at random, what is the probability that it is blue?
Why it works: Total marbles \(=3+5+2=10\). Blue marbles \(=5\). Probability \(=\frac{5}{10}=\frac{1}{2}\).
Answer: \(\frac{1}{2}\)
Introduction to Probability becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A bag contains \(3\) red marbles, \(5\) blue marbles, and \(2\) green marbles. If one marble is drawn at random, what is the probability that it is blue?
Answer C: \(\frac{1}{2}\)
Total marbles \(=3+5+2=10\). Blue marbles \(=5\). Probability \(=\frac{5}{10}=\frac{1}{2}\).
Which event is certain to happen?
Answer C: Flipping a coin and it landing on heads or tails.
Certain events have probability 1. Only choice C must happen every time a coin is flipped.
A spinner is divided into \(4\) equal sections colored red, blue, green, and yellow. What is the probability of spinning red or blue?
Answer C: \(0.5\)
Each color has probability \(\frac{1}{4} = 0.25\). Red or blue \(= 0.25 + 0.25 = 0.5\).
A jar contains \(8\) chocolate chip cookies and \(2\) oatmeal cookies. If you pick one cookie at random, what is the probability you pick an oatmeal cookie?
Answer A: \(\frac{1}{5}\)
Total cookies \(=8+2=10\). Oatmeal cookies \(=2\). Probability \(=\frac{2}{10}=\frac{1}{5}\).
The spinner above is spun. Which probability is impossible?
Answer C: \(P(\text{Purple}) = 0.25\)
The spinner has only red, blue, yellow, and green sections. Purple is impossible because it does not appear on the spinner.
A standard six-sided die is rolled. What is the probability of rolling a number less than or equal to 4?
Answer C: \(\frac{2}{3}\)
Favorable outcomes: \(1, 2, 3, 4\) (four outcomes). Total outcomes: \(6\). Probability \(= \frac{4}{6} = \frac{2}{3}\).
A bag contains \(6\) white socks and \(4\) black socks. If one sock is drawn randomly, what is the probability of drawing a black sock expressed as a decimal?
Answer A: \(0.4\)
Total socks \(= 10\). Black socks \(= 4\). Probability \(= \frac{4}{10} = 0.4\).
The probability that it rains tomorrow is \(\frac{3}{5}\). What is the probability that it does not rain?
Answer B: \(\frac{2}{5}\)
Using complementary events: \(P(\text{not rain}) = 1 - P(\text{rain}) = 1 - \frac{3}{5} = \frac{2}{5}\).
A number from 1 to 20 is selected at random. What is the probability that the number is even?
Answer D: \(\frac{1}{2}\)
Even numbers from 1 to 20: \(2, 4, 6, 8, 10, 12, 14, 16, 18, 20\) (10 outcomes). Probability \(= \frac{10}{20} = \frac{1}{2}\).
A deck of cards has \(52\) cards: \(13\) hearts, \(13\) diamonds, \(13\) clubs, and \(13\) spades. What is the probability of drawing a heart?
Answer D: \(\frac{1}{4}\)
Hearts in deck \(= 13\). Total cards \(= 52\). Probability \(= \frac{13}{52} = \frac{1}{4}\).
An event has probability \(0.75\). What is the probability of the complement (the event not occurring)?
Answer B: \(0.25\)
Complement probability \(= 1 - 0.75 = 0.25\) or \(25\%\).
