Question

Imran drives, walks or cycles to work depending on the weather.

 If it is raining, he will always drive to work.
 If it is not raining, then he will cycle to work unless it is windy then he walks.

The probability it is raining on any particular day is 0.3
The probability it is not raining but it is windy is 0.18

a) Write down the probability that Imran drives to work.

b) Work out the probability that Imran drives to work two days in a row.

c) Work out the probability that Imran cycles to work.

Answer 1

Part a)

It is given that : If it is raining, Imran will always drive to work. The probability of raining is given to be 0.3.
Therefore, the probability that Imran will drive to work on any particular day is equal to 0.3.

Part b)
Probability of raining on 2nd day is independent of the raining on 1st day. So the probability of raining on 2nd day will also be equal to 0.3

The probability that it will rain on two consecutive days will be the product of probabilities that it will rain on 1st day and 2nd day.

So, Imran drives to work two days in a row if it rains two days in a row.

Thus the probability that Imran drives to work two days in a row = 0.3 x 0.3 = 0.09

Part c)
Imran will cycle to work if it is not raining and it is not windy.

The probability that it is not raining but it is windy is 0.18. So the probability that it is not raining but it is not windy is 1 - 0.18 = 0.82

Therefore, the probability that Imran will cycle to work = 0.82