Mathematical Methods — Question 17

QCAA 2021, Paper 1 · 3 marks

Q17 · 2021 · Technology-freeComplex familiar3 marks

QUESTION 17 (3 marks)

In any five-day working week Leonardo either catches a bus to work or uses another form of transportation. On average, he catches the bus to work on three of the five days. His decision on any given day is independent of his decision on any other day. Determine the probability that Leonardo catches a bus to work on exactly one day in a given five-day working week.

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WORKED SOLUTION

QCAA guide · typeset solution

3 marks

ANSWER

\dfrac{48}{625}

Worked solution

Using a binomial distribution,

n=5

p=\frac35

and

q=\frac25

. Therefore

P(X=1)=\binom51\left(\frac35\right)\left(\frac25\right)^4=\frac{48}{625}.

correctly determines the values for p and n

[1 mark]

establishes expression for the required probability

[1 mark]

determines probability

[1 mark]

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Mathematical Methods — Question 17

QUESTION 17 (3 marks)

QCAA guide · typeset solution

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