A market research assistant watches five customers as they leave a store. He records whether the customer is carrying a store bag that indicates any customer made a purchase. He writes down a yes or a no for each. The sample space consists of all possible sequences of yes or no for these five customers. Define the events.

A = {first two shoppers both have a bag}

B = {last two shoppers both have a bag}

C = {last three shoppers all have a bag}

The probability that both events B and C occur is equal to P(B).