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Please help me solve this question:
Consider a shopper will choose either brand A or brand B.
On each purchase, the probability that he will choose the same brand that he chose on his last preceding purchase is 1/3,
and the probability that he will switch brands is 2/3.
Suppose that on his first purchase the probability that he will choose brand A is 1/4
and the probability that he will choose brand B is 3/4.
What is the probability that his second purchase will be brand B?
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The key step is to understand and to write this logical expression
P(second purchase is brand B) = P(1st purchase is brand A)*P(for 2-nd purchase switch from A to B) +
+ P(1-st purchase is brand B)*P(for 2-nd purchase choose B again).
As soon as you understand it, you substitute the given values into the expression and calculate
P(second purchase is brand B) = + = + = = . ANSWER
Solved and explained.