Probability

OCR

GCSE

Probability in Further Mathematics necessitates the rigorous application of conditional logic and set notation to model multi-stage events. Candidates must distinguish between independent and mutually exclusive events, utilizing tree diagrams to calculate joint probabilities and the conditional formula P(A|B) = P(A ∩ B) / P(B). Mastery involves solving complex 'without replacement' scenarios and applying Bayesian-style reasoning to determine inverse probabilities from outcome data.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

What You Need to Demonstrate

Key skills and knowledge for this topic

Award M1 for a correct tree diagram structure with at least one pair of branches labeled with correct probabilities
Award M1 for correctly identifying the denominator reduction (n-1) in the second stage for selection without replacement
Award M1 for the process of multiplying probabilities along branches to find P(A and B)
Award M1 for summing the products of mutually exclusive branches (e.g., P(Red, Blue) + P(Blue, Red))
Award A1 for forming a correct algebraic equation by equating the total probability to a given value (e.g., forming a quadratic)

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You correctly set up the tree, but check your denominators for the second pick — did the total number of items change?"
"Remember that 'one of each color' can happen in two ways (Red-Blue OR Blue-Red); you only calculated one path."
"Good use of algebra, but ensure you expand (n)(n-1) correctly when forming your equation."
"To secure the final marks, show the full substitution into the quadratic formula or factorization steps clearly."

Marking Points

Key points examiners look for in your answers

Award M1 for a correct tree diagram structure with at least one pair of branches labeled with correct probabilities
Award M1 for correctly identifying the denominator reduction (n-1) in the second stage for selection without replacement
Award M1 for the process of multiplying probabilities along branches to find P(A and B)
Award M1 for summing the products of mutually exclusive branches (e.g., P(Red, Blue) + P(Blue, Red))
Award A1 for forming a correct algebraic equation by equating the total probability to a given value (e.g., forming a quadratic)

Examiner Tips

Expert advice for maximising your marks

💡For 'at least one' questions, calculate 1 - P(none) to save time and reduce calculation errors
💡When the question involves unknown numbers of items (e.g., 'n' red balls), write the probabilities algebraically immediately on the tree branches
💡Always check that the probabilities on any set of branches originating from a single point sum to exactly 1

Common Mistakes

Pitfalls to avoid in your exam answers

Failing to reduce the denominator by 1 for the second selection in 'without replacement' scenarios, treating it as independent
Calculating only one order for mixed events (e.g., finding P(Red then Blue) but ignoring P(Blue then Red))
Algebraic errors when multiplying fractions involving unknowns, such as failing to multiply (x)(x-1) correctly
Adding probabilities along the branches instead of multiplying them

Key Terminology

Essential terms to know

Conditional Probability and Notation P(A|B)

Independent vs Mutually Exclusive Events

Tree Diagrams for Dependent Events

Algebraic Probability Solving

Likely Command Words

How questions on this topic are typically asked

Work out

Calculate

Show that

Determine

Solve

Practical Links

Related required practicals

•{"code":"Contextual Application","title":"Quality Control Sampling","relevance":"Calculating risk of defective items in batch testing without replacement"}

Ready to test yourself?

Practice questions tailored to this topic