At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are lorries. If every vehicle is equally likely to leave, find the probability of:

a) a van leaving first.

b) a lorry leaving first.

c) a car leaving second if either a lorry or van had left first.

julianashleeTyro

Since all vehicles have equal chance of leaving, the probability of a van leaving first is given by the number of vans divided by the total number of vehicles.

That is, probability of a van leaving first = .

Similarly, theprobability of a lorry leaving first is given by the number of lorries divided by the total number of vehicles.

That is, probability of a van leaving first = .

The probability of a car leaving second if (given that) a lorry or a van left first is given by the probability that a lorry or a van left first and a car left second divided by the probability that a lorry or a van left first.

The probability that a lorry or a van left first is given by 0.3 + 0.1 = 0.4.

The probability that a lorry or a van left first and a car left second is given by .

Therefore, the probability of a car leaving second if a lorry or a van left first is given by .