Reach for the Star

Probability and expected frequency · Optional extension

L049 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

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

Reveal a worked check after attempting

Estimated P(H)=78/120=0.65; expected count=260.

Deep challenge

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

Reveal a worked check after attempting

It is a long-run prediction; random variation means the observed count may differ.

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?