Why isn't the answer to TMUA-P1-MSTAT-016 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MSTAT-016 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MSTAT-016?

No — calculators are banned in the TMUA. TMUA-P1-MSTAT-016 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MSTAT-016?

TMUA-P1-MSTAT-016 is Paper P1 · Statistics and probability (specification code M-Stat), level 3. Drill more of the same topic from this page.

TMUA-P1-MSTAT-016 — Paper P1 · Statistics and probability · Level 3

P1M-StatLevel 3~240s target

Spec: M-Stat · No calculator · ~240s

A biased coin lands heads with probability

\frac{1}{3}

. It is tossed twice. Given that at least one toss lands heads, what is the probability both land heads?

Options

$\frac{1}{9}$
$\frac{1}{4}$
$\frac{1}{3}$
$\frac{1}{5}$
$\frac{2}{5}$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: mprob-conditional, conditional-probability. Name the trap first, work the stem by hand, then open the solution below.

Show solution

P(H,H) = \frac{1}{9}

and

P(\text{at least one head}) = 1 - \left(\frac{2}{3}\right)^2 = \frac{5}{9}

, so the conditional probability is

\frac{1/9}{5/9} = \frac{1}{5}

.
Trap:

\frac{1}{9}

is the unconditional probability — it forgets to divide by the shrunken sample space.

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Same topic · same level

P1M-StatLevel 3

TMUA-P1-MSTAT-006

1 in 10 people carries a trait. A test is 90\% accurate both ways (true-positive and true-negative rates are 0.9 ). Give…

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Open TMUA-P1-MSTAT-006 →

Same trap: mprob-conditional

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Open TMUA-P1-MSTAT-008 →

TMUA-P1-MSTAT-016 — Paper P1 · Statistics and probability · Level 3

Options

Keep practising

Master Statistics and probability

TMUA-P1-MSTAT-016 — Paper P1 · Statistics and probability · Level 3

Options

Keep practising

Master Statistics and probability