Question

The manager at Mugg & Bean has been recording the behaviour of their customers with regards to coffee and muffins. The manager established that that the probability that a customer will buy a cup of coffee is 0.8. A customer buys a muffin 50% of the time when a cup of coffee is bought. but only 10% of the time when a cup of coffee is not bought. What is the probability of buying a muffin, when first buying a cup of coffee?

Answer 1

Let M represent the muffin,

let C represent the coffee.

Given that the probability that a customer will buy a cup of coffee is 0.8, this implies that

`Pr(C)=0.8`

A customer buys a muffin 50% of the time when a cup of coffee is bought. This implies that

`Pr(M|C)=(50)/(100)=(1)/(2)`

10% of the time when a cup of coffee is not bought. This implies that

`Pr(M|C^(\prime))=(10)/(100)=(1)/(10)`

The probability of buying a muffin,when first buying a cup of coffee is evaluated as