Reach for the Star | GCSE Mathematics

L049: Probability and expected frequency

Objective

Use the probability scale and calculate expected frequency.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Probability and expected frequency
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for probability and expected frequency.

Core practice

A biased coin shows heads 78 times in 120 tosses. Estimate heads in the next 400 tosses.

Reasoning

Why is an expected frequency of 26 not a guarantee of exactly 26 successes?

Exam-style

A probability problem is presented with two stages. Complete the representation, calculate the probability and explain any assumption.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L049: Probability and expected frequency

Objective: Use the probability scale and calculate expected frequency.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the outcomes systematically, used the correct probability rule and checked that the probabilities or frequencies were consistent.

Even Better If (EBI)

I will show the sample space, branch or set reasoning explicitly, state any dependence or condition and check totals before giving the final probability.

Stretch and deep challenge

Stretch: A biased coin shows heads 78 times in 120 tosses. Estimate heads in the next 400 tosses.

Deep challenge: Why is an expected frequency of 26 not a guarantee of exactly 26 successes?