Find the probability that the third head occurs on toss 10.

01 / Standard#Your turn

Official paper · jm01-2023 · II.1(c) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Exactly two heads must occur among the first nine tosses.

Hint 2

Fix a head on the last toss.

Worked solution

(3/4)⁹.

Checks and common pitfalls: Choosing three heads anywhere in ten does not enforce the last-head time.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Count the choices for the earlier two heads.
$P=\binom92(1/4)^2(3/4)^7(1/4)$
Simplify the powers.
$P=\frac{36\cdot3^7}{4^{10}}=(3/4)^9$

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

2023 JM01