L073 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.
Two independent events have probabilities 0.4 and 0.7. Find P(both) and P(neither).
Both=0.28; neither=0.6×0.3=0.18.
Toss a biased coin with P(H)=0.7 three times. Find P(exactly two heads).
3×0.7²×0.3=0.441.
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.
I represented the outcomes systematically, used the correct probability rule and checked that the probabilities or frequencies were consistent.
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: 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).