Probability

Question 1

A raffle is selectived out of 30 positively behaving students at Bacchus Marsh College, given there are 7 prizes, and 12 of the students are boys. What is the probability that more than 6 prizes go to girls?

2 marks

Question 2

A die is loaded in the following way and rolled 6 times,
- 6 has a k chance of being rolled
- 5 has a ⅕ chance of being rolled
- 4 has a 2k ÷ 15 chance of being rolled
- 3 has a k ÷ 5 chance of being rolled
- 2 has a k² ÷ 10 chance of being rolled
- 1 has a ⅔ chance of being rolled
Given that each dice roll is independent, what is the probabilty of rolling exactly five 2s?

4 marks

Answer 2

k ≈ 0.099
X ~ Binomial
⇒ Pr(2 chosen 5 times) = nCr(6,5) × (k² ÷ 10)⁵ × (1 - k² ÷ 10)
*≈ 5.56559 × 10⁻¹⁵

Question 3

The probability of a thunderstorm happening is one tenth on any given day, likewise, the probability of a bushfire is one hundredth. If the chance of both a thunderstorm and a bushfire occuring on the same day is 30%, what is the chance that a bushfire occurs, given there is a thunderstorm?

3 marks

Question 4

Tasmania Jones runs a casino. If any person’s chance of winning is 1%, and if they win, they win 300% of their gamble, what is the estimated profit for Jones if 1,000 people bet? (express in terms of x)

3 marks

Question 5

Let μ equal the mean of the following discrete probability table:
Pr(0) = 6q
Pr(1) = 2q²
Pr(2) = ½
Pr(3) = 2q
Pr(4) = q³
What is the value of μ²?

Evaluate q to 2 decimal places before calculating the mean

4 marks

Question 6

Write a pseudocode dice generator, and run it until i ← 15. What is the difference between the true probability and the data extrapolated?

the rand(0, 1,… n) function prints a random result from 1 to n

6 marks

Question 7

Jim has a drawer of three different coloured socks, purple, green, and orange. If Jim has 2 green socks, 3 purple socks, and 1 orange sock, what is the probability that he pulls out 2 green socks followed by 2 purple socks whenever he pulls out all 6 socks in a row?

Question 8

The Bouncy Ball Company (BBC) produces downballs. For quality control, downballs must be able to bounce up to three quarters of their original height in order to be sold. These ‘anomalies’ have a 1/x chance of occuring. If an inspector chose 6 balls, and the probability that 2 of them were damaged was more than 0.3, what is the minimum value for x?

4 marks