Topic Review — Probability

Review Questions

1. List the sample space for each experiment: Fluency

   1. Flipping a coin
   2. Rolling a standard six-sided die
   3. Picking a letter at random from the word MATHS
   4. Picking a day of the week that starts with the letter T

2. A bag contains 5 red, 3 blue, and 2 yellow marbles (10 total). Find the probability of picking: Fluency

   1. A red marble (write as a fraction)
   2. A blue marble (write as a percentage)
   3. A yellow marble (write as a decimal)
   4. A marble that is not red (write as a fraction)

3. A spinner has 12 equal sections: 4 green, 5 orange, and 3 purple. Find: Understanding

   1. P(green) as a simplified fraction
   2. P(purple) as a decimal
   3. P(not orange) as a percentage
   4. Are green and orange equally likely? Explain.

4. Use the complement to find each probability: Understanding

   1. P(rain) = 0.35. Find P(no rain).
   2. A bag contains only red and blue marbles. P(red) = 37. Find P(blue).
   3. P(catching the bus) = 60%. Find P(not catching the bus).

5. Probability problem solving: Problem Solving

   1. Which is more likely: rolling a number greater than 4 on a die, or flipping heads on a coin? Show your working.
   2. P(red marble) = 0.4. If there are 20 marbles in total, how many are red?
   3. Design a spinner with 8 equal sections where P(yellow) = 14 and P(blue) = 38. How many sections of each colour?

6. A card is drawn from a standard deck of 52 cards. Find: Understanding

   1. P(a heart) as a fraction
   2. P(a king) as a fraction
   3. P(a red card) as a percentage
   4. P(not a club) as a fraction

7. Place each event on the probability scale from 0 to 1: Fluency

   1. Rolling a 7 on a standard six-sided die
   2. Getting an even number when rolling a die
   3. The sun will rise tomorrow
   4. Picking a black card from a deck of 52 cards

8. A box contains 6 red, 4 green, and 5 blue counters. One counter is picked at random. Understanding

   1. How many counters are there in total?
   2. Find P(red) as a fraction in simplest form.
   3. Find P(green or blue) as a fraction.
   4. Two counters of the same colour are removed. Which colour would make P(red) = 12? Is this possible?

9. A game uses a spinner with sections labelled 1, 2, 2, 3, 3, 3. Problem Solving

   1. What is the probability of spinning a 3?
   2. What is the probability of spinning a number less than 3?
   3. If the spinner is spun 60 times, how many times would you expect to get a 2?
   4. Is this a fair game if you win a point for spinning 3 and lose a point for spinning 1 or 2? Explain.

10. Experimental probability: Jade flips a coin 40 times and gets heads 18 times. Understanding

    1. What is the experimental probability of getting heads?
    2. What is the theoretical probability of getting heads?
    3. Are the experimental and theoretical probabilities the same? Explain why they might differ.