A decision has a 0.5 chance of a 100,000 payoff and a 0.5 chance of a 40,000 payoff. Calculate its expected value. [2 marks]

OCR OCR H431/02 2018-style practice: A project has two options. Option A: a probability of 0.7 of a 200,000 payoff and 0.3 of a 50,000 payoff. Option B: a certain payoff of 140,000. Calculate the expected value of Option A and recommend which option to choose. (6)

A Component 2 calculation rewarding the formula, correct substitution and a recommendation. Expected value of Option A = (0.7 × 200,000) + (0.3 × 50,000) = 140,000 + 15,000 = 155,000. Compare with Option B's certain 140,000. On expected value alone, Option A is preferred because 155,000 > 140,000. Markers reward working and units, plus a brief judgement: a risk-averse firm short of cash might still pick the certain 140,000, since the expected value ignores the spread of outcomes. The common error is to forget to multiply each payoff by its probability before adding.

EnglandBusinessSyllabus dot point

How do businesses use quantitative techniques to make decisions?

Quantitative decision-making techniques, including decision trees and expected values, and critical path analysis to plan and schedule projects, together with the value and limitations of each technique.

A focused answer to the OCR A-Level Business theme on quantitative decision making, covering decision trees and expected monetary values, critical path analysis and the float, and the value and limitations of each technique with worked calculations.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this theme is asking
Decision trees
Critical path analysis
The value and limitations of CPA
Examples in context
Try this

What this theme is asking

OCR wants you to use two quantitative decision tools, decision trees (with expected values) and critical path analysis (CPA), and to judge how useful each is. Both appear as calculation questions in Components 2 and 3, usually followed by a recommendation or evaluation.

Decision trees

The firm chooses the option with the highest net expected value (expected value minus the cost of the option). Decision trees force probabilities and payoffs to be stated explicitly, which disciplines the decision, but the probabilities are usually estimates, the payoffs are forecasts, and the method assumes the firm is risk-neutral (it ignores how much a bad outcome would hurt).

Worked example: choosing between two options with a decision tree

A firm chooses between launching a new product (cost $\pounds 60{,}000$ ) or extending the old one (cost $\pounds 20{,}000$ ).

step 1: expected value of the launch

The launch has a $0.6$ chance of $\pounds 300{,}000$ and a $0.4$ chance of $\pounds 80{,}000$ .

\text{EV} = (0.6 \times 300{,}000) + (0.4 \times 80{,}000) = 180{,}000 + 32{,}000 = \pounds 212{,}000

step 2: net value of the launch

Net value $= 212{,}000 - 60{,}000 = \pounds 152{,}000$ .

step 3: expected value and net value of the extension

The extension has a $0.7$ chance of $\pounds 150{,}000$ and a $0.3$ chance of $\pounds 60{,}000$ .

\text{EV} = (0.7 \times 150{,}000) + (0.3 \times 60{,}000) = 105{,}000 + 18{,}000 = \pounds 123{,}000

Net value

= 123{,}000 - 20{,}000 = \pounds 103{,}000

step 4: decide

The launch has the higher net expected value ( $\pounds 152{,}000$ versus $\pounds 103{,}000$ ), so on the numbers the firm launches. A cautious, cash-short firm might still prefer the cheaper, less risky extension, because the expected value hides the spread of outcomes.

Critical path analysis

CPA works out, for each activity, the earliest start time (EST) and the latest finish time (LFT). The float is the spare time a non-critical activity has before it would delay the project:

\text{Float} = \text{LFT} - \text{duration} - \text{EST}

Activities on the critical path have zero float. Knowing this lets a manager schedule resources, identify which delays matter, and consider bringing activities forward (running them in parallel) to shorten the project.

The value and limitations of CPA

CPA forces a project to be planned in detail, identifies the activities that cannot slip, and supports tighter control and resource scheduling. But the network is only as reliable as its time estimates, which are uncertain for complex projects; it does not guarantee the resources will be available when needed; and it must be revised as circumstances change. It is a planning aid, not a guarantee.

Examples in context

A construction firm uses CPA to schedule a build so that, for example, foundations (critical) are never delayed while landscaping (with float) can wait. A manufacturer deciding whether to invest in new machinery might use a decision tree to weigh a high-payoff, uncertain automation project against a safer, smaller upgrade. A retailer planning a store refit uses CPA to keep the closure as short as possible, since every extra day shut costs sales.

Try this

Q1. A decision has a $0.5$ chance of a $\pounds 100{,}000$ payoff and a $0.5$ chance of a $\pounds 40{,}000$ payoff. Calculate its expected value. [2 marks]

Cue. $(0.5 \times 100{,}000) + (0.5 \times 40{,}000) = \pounds 70{,}000$ .

Q2. Analyse one benefit to a project manager of identifying the critical path. [6 marks]

Cue. It shows which activities cannot slip without delaying the whole project, so the manager focuses resources and control there, developed as a chain in context.

Exam-style practice questions

Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

OCR H431/02 20186 marksA project has two options. Option A: a probability of

0.7

of a

\pounds 200{,}000

payoff and

0.3

of a

\pounds 50{,}000

payoff. Option B: a certain payoff of

\pounds 140{,}000

. Calculate the expected value of Option A and recommend which option to choose. (6)

Show worked answer →

A Component 2 calculation rewarding the formula, correct substitution and a recommendation. Expected value of Option A $= (0.7 \times 200{,}000) + (0.3 \times 50{,}000) = 140{,}000 + 15{,}000 = \pounds 155{,}000$ . Compare with Option B's certain $\pounds 140{,}000$ . On expected value alone, Option A is preferred because $\pounds 155{,}000 > \pounds 140{,}000$ . Markers reward working and units, plus a brief judgement: a risk-averse firm short of cash might still pick the certain $\pounds 140{,}000$ , since the expected value ignores the spread of outcomes. The common error is to forget to multiply each payoff by its probability before adding.

OCR H431/02 202312 marksAssess the value of critical path analysis to a UK construction firm managing a large building project. (12)

Show worked answer →

A 12-mark "Assess" on a four-level grid. For: critical path analysis identifies the sequence of activities that determines the minimum project duration (the critical path) and the float on non-critical tasks, so the firm can schedule resources, bring activities forward and spot which delays will push back completion. Chain: knowing the critical path lets the manager focus attention on the tasks that cannot slip, reducing the risk of late-completion penalties. Against: the network is only as good as the time estimates, which for a complex build are uncertain; it does not guarantee resources are available, and it must be revised as the project changes. Evaluation: CPA is valuable for planning and control but is a model resting on estimates, so it should be updated and combined with experienced judgement. A judged conclusion reaches the top band.

Related dot points

Sources & how we know this

OCR A-Level Business (H431) specification — OCR (2015)