Reach for the Star

Probability trees and combined events · Optional extension

L073 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

Two independent events have probabilities 0.4 and 0.7. Find P(both) and P(neither).

Reveal a worked check after attempting

Both=0.28; neither=0.6×0.3=0.18.

Deep challenge

Toss a biased coin with P(H)=0.7 three times. Find P(exactly two heads).

Reveal a worked check after attempting

3×0.7²×0.3=0.441.

Recall & Review: feedback and extension integration

Lesson L073: Probability trees and combined events

Objective: Use probability trees and combine event probabilities.

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: Two independent events have probabilities 0.4 and 0.7. Find P(both) and P(neither).

Deep challenge: Toss a biased coin with P(H)=0.7 three times. Find P(exactly two heads).