(solution) At a certain store the manager has determined that 30%of

(solution) At a certain store the manager has determined that 30%of

At a certain store the manager has determined that 30%of customers pay cash and 70%of customers pay by debit card. (No other method of payment is accepted, and no one is allowed to pay with both cash and a debit card.) Let M be the event that a customer pays cash and D is the event that a customer pays by debit card.

1. Let S be the event that both customers use the same method of payment. Find P(S).

2. Let T be the event that both customers use different methods of payment. Find P(T) by two different methods: by using the complement rule and by using the branches of the tree. Your answers should be the same with both methods.

3. Let U be the event that the second customer uses a debit card. Find P(U).

Let A be the event that there are at least two tails. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? 

a) Events 
At a certain store the manager has determined that 30%of customers pay cash and 70%of
customers pay by debit card. (No other method of payment is accepted, and no one is allowed to
pay with both…