For this coin, find the probability that the first head occurs on toss 10.

01 / Standard#Your turn

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The first nine tosses must be tails.

Hint 2

The tenth toss must be a head.

Worked solution

3⁹/4¹⁰.

Checks and common pitfalls: No binomial coefficient is needed because the head position is fixed.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Specify the unique outcome pattern.
$T^9H$
Multiply the independent probabilities.
$P=(3/4)^9(1/4)=3^9/4^{10}$

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

2023 JM01