Mixed practice Problem set B

The table shows the fuel type and colour of cars in a car park.

1. (a) Find the probability that a car chosen at random is silver.
2. (b) Find the probability that a car chosen at random is a hybrid.
3. (c) Find the probability that a car chosen at random is a silver hybrid.

Events A and B are such that

1. (a) \(P(A)=0.45\), \(P(A\cap B)=0.2\) and \(P(A\cup B)=0.75\). Find \(P(B)\).
2. (b) \(P(A)=0.5\), \(P(A\cup B)=0.85\) and \(P(B')=0.55\). Find \(P(A\cap B)\).

A bag holds 10 red sweets and 5 green sweets. Two sweets are taken out at random without replacement. Find the probability that they are different colours.

A sixth-form common room records the hot drink chosen by students.

1. (a) Find the probability that a student chooses tea, given that the student is in Year 12.
2. (b) Find the probability that a student chooses tea, given that the student is in Year 13.
3. (c) Determine whether choosing tea is independent of year group. Justify your answer.

Of 48 houses on an estate, 26 have solar panels, 11 have solar panels and a heat pump, and 10 have neither.

1. (a) Find the number of houses that have a heat pump but do not have solar panels.
2. (b) Find the probability that a house chosen at random has a heat pump.
3. (c) Given that a house has a heat pump, find the probability that they have solar panels.

A courier delivers a parcel by van with probability 0.7 and otherwise by bike. The parcel arrives damaged with probability 0.04 by van and 0.01 by bike.

1. (a) Find the probability that the parcel goes by van and arrives damaged.
2. (b) Find the probability that the parcel arrives intact.

A quiz team has three members. Each question is answered by one of them, each with probability \(\frac{1}{3}\). The probability that the answer is wrong is 0.08 for Kai, 0.15 for Lu and 0.25 for Max.

1. (a) Find the probability that a question is answered by Max and the answer is wrong.
2. (b) Find the probability that a question is answered correctly.

A factory makes phones and 3% of them are faulty. An automatic check flags 90% of the faulty phones and 6% of the phones that are not faulty. A phone is chosen at random and checked.

1. (a) Find the probability that the phone is flagged.
2. (b) Given that the phone is flagged, find the probability that it is faulty.

Three fair six-sided dice are rolled and the scores are added. Find the probability that the sum is 7.

Events A and B are such that \(P(A)=\frac{3}{4}\), \(P(B|A)=\frac{2}{3}\) and \(P(A\cup B)=\frac{7}{8}\).

1. (a) Find \(P(A\cap B)\).
2. (b) Find \(P(B)\).

The probability that a train is late on Monday is 0.25. If it is late on Monday, the probability that it is late on Tuesday is 0.7. If it is on time on Monday, the probability that it is late on Tuesday is 0.1.

1. (a) Find the probability that the train is late on Tuesday.
2. (b) Given that the train is late on Tuesday, find the probability that it was late on Monday.