Analysis and Approaches for IBDP Maths Ebook 2 | Page 240

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2. Three types of fuels, diesel, gasoline and LPG, are available in a gas station. The
probability that a customer chooses diesel and gasoline are 2 p and p respectively. For
the customers choosing diesel, 45% of them are motorists. For the customers choosing
gasoline, 15% of them are motorists. For the customers choosing LPG, 8% of them are
motorists. Assume that each customer only chooses one type of fuel. A customer is
randomly chosen, and the probability that the customer is a motorist is 0.2015.
(a) Find the value of p .
(b)
Given that the customer chosen is not a motorist, find the probability that he
chooses LPG.
[3]
[3]
3. There are 160 elected councillors in a council, of which 50 are aged 65 or above. All
elected councillors are from one of the three political parties: the National Party, the
Labour Party and the Democratic Party. For the councillors aged 65 or above, q % and
2 q % of them are from the National Party and the Labour Party respectively. For the
councillors aged 64 or below, 1.5 q % and q % of them are from the National Party and
the Labour Party respectively. A councillor is randomly chosen, and the probability that
the councillor belongs to the Labour Party is 0.105.
(a) Find the value of q .
(b)
Given that the councillor belongs to the Democratic Party, find the probability
that he ages 64 or below.
[3]
[3]
4. Machines X , Y and Z produce electronic components in a factory. The ratio of the
number of electronic components produced by machine X to that of machine Y to that
of machine Z is 7 :11: 2. The percentages of defective components produced by
machine X , machine Y and machine Z are 2%, 1% and 3% respectively. An electronic
component is randomly chosen. Given that it is defective, find the probability that it was
not produced by machine X .
[4]
230
SE Production Limited