Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. T

Question

Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. The type of soft drink purchased in 3 consecutive weeks is to be recorded. If a different type of soft drink is purchased than in the previous week, we say that there is a switch. Let X denote the number of switches. Suppose that for each purchase P(B)= (1/2) and the decisions in different weeks are independent. Assign probabilities to the elementary outcomes and obtain the distribution of X .

Write the x-values in ascending order.

The probability distribution of x is:

Table with three blanks under each varaible:

x   |   f(x)

Total | 1

Explanation / Answer

P(X=0) =P(all three week canned drink+all 3 weeks bottled drink) =(1/2)*(!/2)*(!/2)+(1/2)*(!/2)*(!/2) =1/4

P(X=1) =P(first week canned then 2 week bottled+first 2 week canned and than bottled+first week bottled then 2 week canned+first 2 week bottled and than canned)=(1/2)*(!/2)*(!/2)+(1/2)*(!/2)*(!/2)+(1/2)*(!/2)*(!/2)+(1/2)*(!/2)*(!/2)

=1/2

P(X=2)=P(first week caneed then bottled and than canned +first bottled and than canned and than bottled)

=(1/2)*(!/2)*(!/2)+(1/2)*(!/2)*(!/2) =1/2

hence

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