Four Year 12 students want to organise a graduation party. All four students have the same probability, \(P(F)\), of being available next Friday. All four students have the same probability, \(P(S)\), of being available next Saturday. It is given that \(P(F)=\dfrac{3}{10}, P(S\mid F)=\dfrac{1}{3}\), and \(P(F\mid S)=\dfrac{1}{8}\). Kim is one of the four students. --- 2 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) --- --- 3 WORK AREA LINES (style=lined) ---
Probability, 2ADV S1 2022 HSC 15
In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6. The other is a special die with faces marked 1, 2, 3, 5, 5, 5.
One die is randomly selected and tossed.
- What is the probability that the die shows a 5? (1 mark)
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- Given that the die shows a 5, what is the probability that it is the special die? (1 mark)
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Probability, 2ADV S1 2019 MET2 11 MC
`A` and `B` are events from a sample space such that `P(A) = p`, where `p > 0, \ P(B\ text{|}\ A) = m` and `P(B\ text{|}\ A prime) = n`.
`A` and `B` are independent events when
A. `m = n`
B. `m = 1 - p`
C. `m + n = 1`
D. `m = p`
Probability, 2ADV S1 SM-Bank 3
In a workplace of 25 employees, each employee speaks either French or German, or both.
If 36% of the employees speak German, and 20% speak both French and German.
- Calculate the probability one person chosen could speak German if they could speak French. Give your answer to the nearest percent. (1 mark)
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- Calculate the probability one person chosen could not speak French if they could speak German. Give your answer to the nearest percent. (1 mark)
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Probability, 2ADV S1 SM-Bank 4 MC
Probability, 2ADV S1 2017 MET1 8
For events `A` and `B` from a sample space, `P\ (A text(|)B) = 1/5` and `P\ (B text(|)A) = 1/4`. Let `P\ (A nn B) = p`.
- Find `P\ (A)` in terms of `p`. (1 mark)
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- Find `P\ (A prime nn B prime)` in terms of `p`. (2 marks)
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- Given that `P\ (A uu B) <= 1/5`, state the largest possible interval for `p`. (2 marks)
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Probability, 2ADV S1 2014 MET1 9
Sally aims to walk her dog, Mack, most mornings. If the weather is pleasant, the probability that she will walk Mack is `3/4`, and if the weather is unpleasant, the probability that she will walk Mack is `1/3`.
Assume that pleasant weather on any morning is independent of pleasant weather on any other morning.
- In a particular week, the weather was pleasant on Monday morning and unpleasant on Tuesday morning.
Find the probability that Sally walked Mack on at least one of these two mornings. (2 marks)
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- In the month of April, the probability of pleasant weather in the morning was `5/8`.
- Find the probability that on a particular morning in April, Sally walked Mack. (2 marks)
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- Using your answer from part b.i., or otherwise, find the probability that on a particular morning in April, the weather was pleasant, given that Sally walked Mack that morning. (2 marks)
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- Find the probability that on a particular morning in April, Sally walked Mack. (2 marks)
Probability, 2ADV S1 2007 MET1 11
There is a daily flight from Paradise Island to Melbourne. The probability of the flight departing on time, given that there is fine weather on the island, is 0.8, and the probability of the flight departing on time, given that the weather on the island is not fine, is 0.6.
In March the probability of a day being fine is 0.4.
Find the probability that on a particular day in March
- the flight from Paradise Island departs on time (2 marks)
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- the weather is fine on Paradise Island, given that the flight departs on time. (2 marks)
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Probability, 2ADV S1 2015 MET1 8
For events `A` and `B` from a sample space, `P(A | B) = 3/4` and `P(B) = 1/3`.
- Calculate `P(A ∩ B)`. (1 mark)
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- Calculate `P(A′ ∩ B)`, where `A′` denotes the complement of `A`. (1 mark)
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- If events `A` and `B` are independent, calculate `P(A ∪ B)`. (1 mark)
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Probability, 2ADV S1 2009 MET1 5
Four identical balls are numbered 1, 2, 3 and 4 and put into a box. A ball is randomly drawn from the box, and not returned to the box. A second ball is then randomly drawn from the box.
- What is the probability that the first ball drawn is numbered 4 and the second ball drawn is numbered 1? (1 mark)
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- What is the probability that the sum of the numbers on the two balls is 5? (1 mark)
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- Given that the sum of the numbers on the two balls is 5, what is the probability that the second ball drawn is numbered 1? (2 marks)
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Probability, 2ADV S1 2014 MET2 14 MC
If `X` is a random variable such that `P(X > 5) = a` and `P(X > 8) = b`, then `P(X < 5 | X < 8)` is
A. `a/b`
B. `(a - b)/(1 - b)`
C. `(1 - b)/(1 - a)`
D. `(a - 1)/(b - 1)`
Probability, 2ADV S1 2013 MET2 17 MC
`A` and `B` are events of a sample space.
Given that `P(A | B) = p,\ \ P(B) = p^2` and `P(A) = p^(1/3),\ P(B | A)` is equal to
A. `p^3`
B. `p^(4/3)`
C. `p^(7/3)`
D. `p^(8/3)`