Mathematical Methods — Question 2

QCAA 2023, Paper 2 · 1 mark

Q2 · 2023 · Technology-activeSimple familiar1 mark

QUESTION 2

The probability of hitting a bullseye is

\frac1{1250}

. Which expression gives the probability of exactly one bullseye in 10 independent attempts?

(A)

\left(\frac1{1250}\right)^{10}

(B)

10\left(\frac{1249}{1250}\right)^9

(C)

\binom{10}{1}\left(\frac1{1250}\right)\left(\frac{1249}{1250}\right)^9

(D)

1-\left(\frac{1249}{1250}\right)^{10}

ABCD

WORKED SOLUTION

1 mark

ANSWER

C —

\binom{10}{1}\left(\frac1{1250}\right)\left(\frac{1249}{1250}\right)^9

Worked solution

Exactly one success in 10 binomial trials is

\binom{10}{1}p(1-p)^9

with

p=1/1250

; C.

Selects option C.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.