Problem 32E

A retailer sells only two styles of stereo consoles, and experience shows that these are in equal demand. Four customers in succession come into the store to order stereos. The retailer is interested in their preferences.

a List the possibilities for preference arrangements among the four customers (that is, list the sample space).

b Assign probabilities to the sample points.

c Let A denote the event that all four customers prefer the same style. Find P( A).

Solution

Step 1 of 3

a) We have to write the sample space of the experiment

Let R be the person selects the type 1 stereo

Let S be the person selects the type 2 stereo

The no.of customers coming to the store =4

The no.of combinations =42 =16

Now the sample space is

S={(RRRR), (RRRS), (RRSR), (RRSS), (RSRR), (RSRS), (RSSR), (RSSS),

(SRRR), (SRRS), (SRSR), (SRSS), (SSRR), (SSRS), (SSSR), (SSSS)}