Question

A electrical goods retail warehouse concludes from a customer survey that 40% of customers who seek advice from the sales staff buy an appliance and that 20% of those entering the warehouse who do not seek such advice buy an appliance. If 30% of all customers entering the warehouse seek advice, what is the probability that a customer entering the warehouse buys an appliance.?

Answer 1

Let
`c` denote the number of customers.

The number of customers that seek advice is
`0.3c`.

The number of customers that do not seek advice is thusly
`(1-0.3)c=0.7c`

40% of the customers that do seek advice buy a device, denoted with
`0.4\cdot0.3c=0.12c` that is 12% of the total customers here buy a device.

20% of the customers that do not seek advice buy a device, denoted with
`0.2\cdot0.7c=0.14c` so 14% of the total customers here buy a device.

Together, the percentage of customers that will buy an applicance on the end of the day is
`12\%+14\%=26\%`.

So the probability from that follows that when a customer enters the shop there exists a 26% probability that the customer will end up buying a device.

Hope this helps :)