Probability Calculations — Practice

Practice bank for UCAT Decision Making probability questions.

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Quick-Reference: Probability Rules

Basic Probability

$P(A) = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$P(A)=Total number of possible outcomesNumber of favourable outcomes​

Probability always ranges from 0 (impossible) to 1 (certain).

Key Rules

Rule	Formula	When to Use
Complement	$P(\text{not } A) = 1 - P(A)$P(not A)=1−P(A)	"What is the probability it does NOT happen?"
Addition (mutually exclusive)	$P(A \text{ or } B) = P(A) + P(B)$P(A or B)=P(A)+P(B)	Events cannot occur simultaneously
Addition (general)	$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$P(A or B)=P(A)+P(B)−P(A and B)	Events may overlap
Multiplication (independent)	$P(A \text{ and } B) = P(A) \times P(B)$P(A and B)=P(A)×P(B)	One event does not affect the other

"At Least One" Problems

$P(\text{at least one}) = 1 - P(\text{none})$P(at least one)=1−P(none)

This is almost always easier than calculating all the individual cases.

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Common Pitfalls

• Confusing "or" (add) with "and" (multiply)
• Forgetting to subtract the overlap in non-mutually-exclusive "or" problems
• Assuming independence when events are actually dependent
• Not simplifying fractions or converting to percentages when the question requires it

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Strategy

1. Identify whether the question asks for "and," "or," or "at least one"
2. Determine whether events are independent or dependent
3. Apply the correct formula
4. Target: 45–60 seconds

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Practice

Complete the 10 assessment questions.