Question

Each time a shopper chooses a brand of dishwashing liquid for her kitchen, she chooses either Ivory or Palmolive. For the first purchase, the probability that she will chose Ivory is 1/4 (and therefore Palmolive 3/4). For each purchase after the first purchase, the chance is 1/3 that she will choose the same brand as the preceding purchase (and is 2/3 that she will switch brands) What is the probability that her second purchase will be Palmolive? (A = Ivory, B = Palmolive, subscript is which level of purchase)

Answer 1

P(A₁) = 1/4

P(B₁) = 3/4

P(Choosing same brand) = 1/3

P(Switching brand) = 2/3

P(Second purchase is Palmolive), P(B₂) = P(A₁B₂) + P(B₁B₂)

= P(A₁) x P(Switching brand) + P(B₁) x P(Choosing same brand)

= 1/4 x 2/3 + 3/4 x 1/3

= 5/12

= 0.4167