Class Trip Budget: Test the Forecasts

Build uniform models and compare budget predictions with trial results.

Build the Budget Model

A class tests its trip budget using six possible cost plans. These are practice forecasts, not confirmed prices. A selector chooses each plan number with equal probability. Costs are per student.

Trip Cost Plans
Plan	Bus ($)	Meal ($)	Museum ticket ($)
1	12	6	8
2	12	8	8
3	14	6	10
4	12	8	10
5	14	8	10
6	16	8	10

Build the uniform model by assigning the same probability to each of the six plan numbers.

What probability belongs to each individual plan?

The six plans produce five different total costs: $26, $28, $30, $32, and $34. Which model correctly assigns probabilities to these totals?

A. Each of the five totals has probability 1/6.B. Each of the five totals has probability 1/5.C. The $30 total has probability 2/6; each other total has probability 1/6.D. The $34 total has probability 2/6; each other total has probability 1/6.

The class has a budget of $30 per student. A plan is affordable if its total cost is at most $30.

What is the model probability of an affordable plan?

The treasurer wants to flag any plan that has BOTH a $14 bus cost and a $10 museum ticket.

What is the probability that the selected plan is flagged?

The class runs 90 selections using the same model. Each selection starts with all six plans available. A plan is over budget when its total exceeds $30.

According to the model, how many over-budget selections are expected? selections

Read the Trial Log

Use the original six-plan model. All six plans are available on every selection. The table shows results from 60 selections.

Observed Budget Trials
Plan	Selections
1	6
2	9
3	8
4	13
5	10
6	14

What percentage of the 60 selections had a total cost greater than $30? %

Compare the observed number of over-budget selections with the number predicted by the uniform model for these 60 trials.

A. The observed count is 4 selections below the predicted count.B. The observed count is 4 selections above the predicted count.C. The observed count is 10 selections below the predicted count.D. The observed count is 10 selections above the predicted count.

Select every statement supported by the original uniform model and the trial log.

The class plans a new set of 600 selections using the same uniform model. Which statement about the new results is justified?

A. Relative frequencies tend to approach model probabilities, but exact agreement is not guaranteed.B. Each plan must appear exactly 100 times in the new results.C. Plan 1 must appear more often than plan 6 in the new results.D. Relative frequencies must repeat those from the first 60 selections exactly.

Test New Budget Decisions

Each question describes a new test for the same class trip. Identify the equally likely outcomes before calculating.

10.

A trip package costs $32 per student before a museum discount. A practice selector chooses equally among five discount amounts: $0, $2, $4, $6, and $8. The class can spend at most $28 per student.

What is the probability that the discounted package is within budget?

11.

Six bus companies submit quotes. Two quote $180, one quotes $210, and three quote $240. The class tests its budget by choosing one company uniformly at random. What probability should its model assign to a $240 quote?

A. The probability is 1/6 because $240 is one quoted price.B. The probability is 1/2 because three of the six companies quote $240.C. The probability is 1/3 because there are three different quoted prices.D. The probability is 2/3 because two of the three prices are below $240.

12.

Bus travel and museum admission together cost $22 per student. A test chooses equally among meal prices of $6, $7, $8, $9, and $10. The class wants exactly four of these five outcomes to be within budget.

What is the smallest whole-dollar budget per student that gives a probability of 4/5 of covering the total cost? $

13.

For a budget drill, the class uses a fair spinner with 12 equal sectors. Each sector names one expense to review. Bus review must have probability 1/4, museum-ticket review must have probability 1/6, and all remaining sectors will name meal review.

How many sectors must name meal review? sectors

14.

In a separate 600-trial check of the original six-plan selector, plan 6 appears 300 times. Sam says, “Trial results can differ by chance, so there is no reason to inspect the selector.” Compare the model probability with the observed relative frequency. Explain why inspecting the selector is reasonable without claiming that these results prove it is unfair.