Problem Bank | IB Math AISL | Perplex

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1

0 / 7

Let R be the value of a roll on 6-sided die. The probability distribution for R is shown in the following table.

r	1	2	3	4	5	6
P(R=r)	0.1	0.1	p	q	0.2	0.2

Sally rolls the dice 100 times, and records 25 rolls of 6.

Explain why this is not inconsistent with the table.
[1]

Josh plays a game using this dice. He pays $4 to roll the dice, and earns back the value of his roll in dollars.

Determine the value of p and the value of q such that the game is fair.
[6]

2

0 / 8

The masses, in grams, of chocolate bars produced by a factory can be modelled by a normal distribution with mean 100g and standard deviation 0.6g. A chocolate bar can only be packaged if its mass is greater than 99g, otherwise is it melted back into the production line.

Find the probability that a randomly selected chocolate bar is packaged.
[2]

On a given day, the number of chocolate bars packaged is 5000.

Estimate, to the nearest 10, the number of chocolate bars that are melted back that day.
[3]
Given that a bar has a mass of less than 101g, find the probability it will be melted down.
[3]

3

0 / 7

At the end of the 2024 fishing season on Fork Lake, 60 anglers (amateur fishers) were randomly surveyed. They were asked how many bass they caught over the whole season. The information is summarized in the following frequency table:

Number of fish caught	Frequency
0	7
1	12
2	10
3	19
4	k
5	3

Assume that this sample is representative of all anglers in any season, and that all anglers have equal skill.

State the value of k.
[1]
For the 2025 season estimate
1. the probability a randomly selected angler will catch fish,
  [1]
2. the expected number of fish caught by an angler over the season.
  [2]

The U.S Fish and Wildlife Service (USFWS) estimates that the bass population in Lake Fork will grow by 8% between the 2024 and 2025 fishing seasons.

Given that the bass population was 110′000 at the end of the 2024 season, estimate the number of bass in the Lake at the opening of the 2025 season.
[1]

The USFWS wants the bass population to remain unchanged year to year.

How many seasonal fishing permits should be granted in 2025? Give your answer to the nearest hundred.
[2]