Complete the distribution of team A’s score for three independent shots with success probabilities 3/4, 2/3 and 1/2.

01 / Standard#Your turn

Official paper · jm01-2026 · II.1(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Each score is a count of successes.

Hint 2

Multiply three linear probability-generating factors.

Worked solution

For each shooter, use miss probability plus hit probability times t.
$G(t)=\left(\frac14+\frac34t\right)\left(\frac13+\frac23t\right)\left(\frac12+\frac12t\right)$
Expand; the coefficient of t to power k is the probability of score k.
$G(t)=\frac{1+6t+11t^2+6t^3}{24}$

Scores 0,1,2,3 have probabilities 1/24, 1/4, 11/24, 1/4.

Checks and common pitfalls: The three success probabilities differ, so one binomial distribution does not apply to team A.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
For each shooter, use miss probability plus hit probability times t.
$G(t)=\left(\frac14+\frac34t\right)\left(\frac13+\frac23t\right)\left(\frac12+\frac12t\right)$
Expand; the coefficient of t to power k is the probability of score k.
$G(t)=\frac{1+6t+11t^2+6t^3}{24}$

Think first. Reveal a hint when the class is ready.

2026 JM01