Question

Two customers enter a store. Independently, they make decisions to purchase or not to purchase. The following diagram shows how the outcomes can occur and combine with red holding of sequence Customer 1 does not purchase and Customer 2 does not Purchase.

The possible outcome are shown. If the event is the number of purchases, 3 events are possible: 0 purchases, 1 purchase, and 2 purchases.

which one rule applies to the sequence of independent outcomes of Customer 1 and Customer 2?

Answer 1

Simple Multiplication Rule: P(A and B) = P(A)*P(B ) is correct

as A and B are independent

As if all probabilty are equally likely on right side then each one will have 0.25 probabilty

Hence P(1purchase) =purcahse no purchase+no purchase purchase =0.25+0.25=0.5

Simple multiplication rule =P(A and B) =P(A)*P(B)

Neither purcahse 0=0.037*0.037 =0.001369

Both purchase 2 =0.963*0.963 =0.927369

1purcahse 1 =0.037*0.963+0.963*0.037=0.071262

As above events contain all sample space beyond which there is no possible event is there hence sum of their probability is equal to 1

If each of the branch is equally likely, the probability of each branch is 1/4, since there are 5 branches.

P(1 purchase)=, since there are two instances of 1 purchase, each with probability 1/4 of occurance.