The probability that it rains on a given day is 0.15. The probability that a football match is cancelled when it rains is 0.65. If it doesn't rain, the probability that the match is not cancelled is 0.95. What is the chance that the match is cancelled?

The aim here is to find the probability that the football match is cancelled in both the case that it rains and in the case that it doesn't. This helps to break the question down; we can find the probability that the football match is cancelled in rainy conditions, and we can separately find out the probability that it is cancelled when there is no rain. This can be done using a tree diagram. It is given that the chance of rain on the day is 0.15. It is also given that if it does rain, there is a 0.65 probability of the match being cancelled. Using the 'and' rule, we can multiply these two values (0.15*0.65) to find out the probability that the match is called off if it rains, which is 0.0975. Since there is a 0.15 probability that there is rain on a given day, the probability there is no rain must be 0.85 as there can only be either rain or no rain. It is stated that if there is no rain, there is a 0.95 chance of the football match not being cancelled. This means that there is a 0.05 chance the football match is cancelled when there is no rain. Using this, we can find the chance of the match being cancelled in the same way as before - by multiplying 0.85 by 0.05 to give 0.0425. The probability that the match is cancelled when it rains is 0.0975, and the probability that it is cancelled when it does not rain is 0.0425, therefore we can find the total probability that the match is cancelled by adding these two values together to give 0.14.
Answer: 0.14