Independent tosses have P(head)=1/4. Find the probability of at most one head in ten tosses.

01 / Standard#Your turn

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

At most one includes zero heads.

Hint 2

Add the binomial probabilities for 0 and 1.

Worked solution

Probability (13/4)(3/4)⁹.

Checks and common pitfalls: “At most” includes zero, unlike “exactly one”.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Write the two disjoint cases.
$P=(3/4)^{10}+\binom{10}1(1/4)(3/4)^9$
Factor the common term.
$P=\frac{13}4(3/4)^9$

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

2023 JM01