L2 Probability
Question Bank
A standard deck of 52 playing cards is used for a game. The cards are well shuffled.
What is the probability that the first card drawn is NOT a face card (Jack, Queen, or King)?
A jar contains 5 red marbles, 3 blue marbles, and 2 green marbles. A marble is drawn at random, its colour is noted, and it is then placed back into the jar (with replacement).
(a) What is the probability that the first marble drawn is green AND the second marble drawn is blue?
(b) What is the probability that neither of the first two marbles drawn is red?
Four letter tiles are placed into a bag. They read A, P, P, L:
A tile is randomly selected, its letter is noted, and the tile is replaced.
(a) What is the probability that the tile drawn is either a Vowel (A) OR the letter L?
(b) What is the probability that the first tile drawn is a Vowel AND the second tile drawn is a Consonant (P or L)?
Seven number tiles are placed into a bag. They read 1, 2, 3, 4, 5, 5, 6:
Two tiles are drawn at random from the bag without replacement.
(a) What is the probability that the first tile drawn is an Odd number OR the number is greater than 5?
(b) What is the probability that both tiles drawn are the number 5?
A bag contains 4 Red, 2 Yellow, and 4 Blue marbles. A visual representation is shown below:
A single marble is drawn from the bag and NOT replaced. A second marble is then drawn.
(a) What is the probability that both marbles drawn are Red?
(b) What is the probability that the second marble drawn is Blue, given that the first marble drawn was NOT Blue?
Two standard six-sided dice are rolled. The scores on the two dice are noted.
(a) What is the total number of possible outcomes (elements in the sample space) when rolling two six-sided dice? List all the outcomes whose sum is exactly 7.
(b) What is the probability that the sum of the scores is 4 OR 10?
A dart is thrown at a target board which is composed of four regions (A, B, C, D) of equal area, as shown below. The dart is thrown twice, and it is assumed to always hit the board.
(a) What is the probability that the dart lands in region A or B on the first throw AND in region C on the second throw?
(b) What is the probability that the dart lands in the same region on both throws?
Two fair six-sided dice are rolled simultaneously, and the sum of the numbers showing on the top faces is recorded.
(a) Complete the probability distribution table below for the sum of the two dice.
| Sum ($S$) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| $P(S)$ |
(b) Using your probability distribution table, calculate:
(i) $P(S \ge 10)$
(ii) $P(S \text{ is even})$
(iii) The average sum.
A sports coach recorded the number of goals scored by 50 players during a season. The results are shown in the bar chart below.
(a) Complete the probability distribution table below based on the bar chart.
| Number of Goals ($G$) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| $P(G)$ |
(b) Using your probability distribution table, calculate:
(i) $P(G \le 2)$
(ii) $P(G > 3)$
(iii) The mean number of goals.
Two players play a game where two fair six-sided dice are rolled simultaneously. The players score is the absolute difference between the two numbers shown (i.e., the larger number minus the smaller number).
(a) Complete the table below showing all possible absolute differences. The first die result is shown across the top, and the second die result is shown down the side.
| Die 1 | ||||||
|---|---|---|---|---|---|---|
| Die 2 | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | ||||||
| 2 | ||||||
| 3 | ||||||
| 4 | ||||||
| 5 | ||||||
| 6 | ||||||
(b) Using your completed table, create a probability distribution table for the absolute difference, $D$.
| Difference ($D$) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| $P(D)$ |
(c) Using your probability distribution table, calculate:
(i) $P(D \ge 3)$
(ii) $P(D = 0 \text{ or } D = 1)$
(iii) The mean value of the absolute difference
A spinner is divided into six equal sectors coloured Red (R), Green (G), Blue (B), Yellow (Y), Orange (O), and Purple (P). The spinner is spun twice.
(a) What is the probability that the spinner lands on Red at least once?
(b) What is the probability that neither spin lands on Blue.
A dart is thrown at a large circular target board consisting of four concentric scoring regions: Bullseye (Red), Inner Ring (Blue), Middle Ring (Green), and Outer Ring (Yellow). The probability of a dart landing in any region is proportional to the region''s area. A dart always lands on the board.
The areas of the scoring regions are: Bullseye: $40 \text{ cm}^2$, Inner Ring: $60 \text{ cm}^2$, Middle Ring: $80 \text{ cm}^2$, and Outer Ring: $100 \text{ cm}^2$.
(a) What is the probability that a dart lands in either the Middle Ring (Green) or the Outer Ring (Yellow)?
(b) If two darts are thrown independently, what is the probability that one dart lands in the Bullseye (Red) and the other lands in the Inner Ring (Blue)?
A bag contains 5 Red, 3 Green, and 2 Yellow marbles. A visual representation is shown below:
Two marbles are drawn from the bag one after the other without replacement.
(a) What is the probability that both marbles drawn are Green or Yellow?
(b) What is the probability that the two marbles drawn are different colours?
A bag contains 5 blue marbles and 3 green marbles. Three marbles are randomly selected from the bag without replacement.
(a) What is the probability that all three marbles drawn are blue?
(b) What is the probability that exactly two of the three marbles drawn are green?