A bag contains 5 red balls, 4 blue balls and 3 green balls.
(a) (i) Megan picks a ball at random. Write down the probability that the ball is red or blue.
(ii) Megan replaces the ball.
She picks a ball at random, notes the colour and replaces the ball.
She repeats this 60 times.
Calculate the number of times the ball is expected to be red or blue.
(b) Mick picks 2 of the 12 balls at random, without replacement. Calculate the probability that the balls are different colours.
(c) Marie picks balls at random, without replacement, from the 12 balls.
When she picks a green ball she stops.
The probability that she picks a green ball on pick $n$ is $\frac{21}{220}$.
Find the value of $n$.
▶️ Answer/Explanation
(a)(i) $\frac{3}{4}$ (9 balls out of 12 are red or blue)
(a)(ii) 45 (60 × 3/4)
(b) $\frac{47}{66}$
1. Total ways to pick 2 balls: 12C2 = 66
2. Calculate 1 – P(same color) = 1 – (5C2 + 4C2 + 3C2)/66
(c) n = 5
This is found by calculating when P(green on nth pick without replacement) = 21/220
Rama asks a group of students how they travel to school.
The table shows the probability of how a student, chosen at random, travels to school.
(a) Complete the table.
(b) There are 1800 students at the school. Find the expected number of students that walk to school.
▶️ Answer/Explanation
Ans:
(a) Other = 1 – (0.4 + 0.32 + 0.17) = 0.11
(b) Expected number = 1800 × 0.32 = 576 students
For part (a), probabilities must sum to 1. For part (b), multiply total students by walk probability.