Success Homeschool

Secondary 3 Mathematics · Two-step chance experiments

Name: ______________________

Date: ____________

1. How many outcomes are in the sample space when two six-sided dice are rolled?
- ☐ (a) 12
- ☐ (b) 36
- ☐ (c) 6
- ☐ (d) 11
2. A coin is flipped and a six-sided die is rolled. How many outcomes are there?
- ☐ (a) 8
- ☐ (b) 12
- ☐ (c) 6
- ☐ (d) 2
3. Two coins are flipped. What is P(two heads)?
- ☐ (a) 12
- ☐ (b) 14
- ☐ (c) 13
- ☐ (d) 34
4. What does “without replacement” mean?
- ☐ (a) The item is put back before the second draw
- ☐ (b) The item is not put back, so the second draw has one fewer item
- ☐ (c) Both items are drawn from different bags
- ☐ (d) The probabilities stay the same for each draw
5. Two dice are rolled and the numbers added. What is P(total of 10)? Give a fraction in simplest form.
6. Two dice are rolled. What is the probability of rolling a double (both dice the same)? Give a fraction in simplest form.
7. A bag has 4 red and 6 green marbles. Two are drawn WITH replacement. What is P(both green)? Give a fraction in simplest form.
8. The same bag (4 red, 6 green) is used, but two marbles are drawn WITHOUT replacement. What is P(both red)? Give a fraction in simplest form.

Answer sheet

1. 36 — Each die has 6 outcomes, so there are 6 × 6 = 36 combinations.
2. 12 — 2 × 6 = 12 outcomes, such as H1, H2, …, T6.
3. 14 — The sample space is {HH, HT, TH, TT}. Only HH is two heads: 14.
4. The item is not put back, so the second draw has one fewer item — Without replacement, the first item stays out, which changes the probabilities for the second draw.
5. 1/12 — Totals of 10: (4, 6), (5, 5), (6, 4) — 3 of 36 outcomes. 336 = 112.
6. 1/6 — There are 6 doubles (1-1 to 6-6) out of 36 outcomes: 636 = 16.
7. 9/25 — P(G) = 610 each time. 610 × 610 = 36100 = 925.
8. 2/15 — 410 for the first red, then 3 red of the 9 left: 39. 410 × 39 = 1290 = 215.