Geometric Probability and Conditional Probability: math test, Grade 10 – download the PDF

1 Counting / 3 pts

A coach has 9 players. (a) In how many ways can a captain and then a vice captain be chosen? (b) In how many ways can 3 players be chosen for a relay team? (c) Explain why the two answers differ.

2 Geometric probability / 4 pts

A rectangular board is 40 cm by 30 cm and has a circle of radius 10 cm drawn entirely inside it. A dart lands at a random point of the board. (a) Find the probability that it lands in the circle (exact value, then a decimal rounded to three places). (b) Find the probability that it does not. (c) A traffic light is green for 40 s, yellow for 5 s and red for 35 s in each cycle. At a random moment, what is the probability that the light is red?

3 Walking or riding / 4 pts

A survey of 120 students gave this table.

(a) Find the row and column totals. (b) Find \(P(\text{walks})\) and \(P(\text{walks}\mid\text{Grade 10})\). (c) Are “walks” and “Grade 10” independent? Justify.

4 Union and complement / 3 pts

For events \(A\) and \(B\): \(P(A)=0.55\), \(P(B)=0.4\), \(P(A\cap B)=0.25\). Find (a) \(P(A\cup B)\), (b) the probability that neither occurs, (c) \(P(A\mid B)\).

5 Spinner and die / 3 pts

A spinner lands on red with probability 0.3. It is spun once and a fair die is rolled once, independently. Find (a) \(P(\text{red and even})\), (b) \(P(\text{red or even})\), (c) the probability that at least one red appears when the spinner is spun twice (independent spins).

6 Draws without replacement / 3 pts

A bag has 4 green and 6 yellow balls. Two are drawn without replacement. Find (a) \(P(\text{both green})\), (b) \(P(\text{second green}\mid\text{first yellow})\), (c) \(P(\text{one of each color})\).