Team B also has three independent shots, each with probability 3/4. Find the probability that the total score is three and B beats A.

01 / Standard#Your turn

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

List score pairs (A,B) satisfying both conditions.

Hint 2

Only (0,3) and (1,2) qualify.

Worked solution

Find B’s probabilities with the binomial formula.
$P(B=3)=\frac{27}{64},\quad P(B=2)=\binom32\left(\frac34\right)^2\frac14=\frac{27}{64}$
Independence allows multiplication; the two disjoint cases are then added.
$P=\frac1{24}\frac{27}{64}+\frac14\frac{27}{64}=\frac{63}{512}$

63/512.

Checks and common pitfalls: Total score three alone would also include pairs where A wins.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find B’s probabilities with the binomial formula.
$P(B=3)=\frac{27}{64},\quad P(B=2)=\binom32\left(\frac34\right)^2\frac14=\frac{27}{64}$
Independence allows multiplication; the two disjoint cases are then added.
$P=\frac1{24}\frac{27}{64}+\frac14\frac{27}{64}=\frac{63}{512}$

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

2026 JM01