A super market analysed its most recent sales and determined the relationship between the way a customer paid for the item and the price category of the item. The joint probabilities in the following table were calculated.
|
Size of purchase
|
Method of payment
|
|
Cash
|
Credit card
|
Debit card
|
|
Under $20
|
0.23
|
0.03
|
0.04
|
|
$20-$100
|
0.05
|
0.21
|
0.09
|
|
Over $100
|
0.02
|
0.23
|
0.10
|
(a) Find the probability that a credit card purchase was over $100.
(b) Determine the proportion of purchase made by credit and debit cards.
(c) Are the event 'payment by cash' and 'purchase of over $100' mutually exclusive? Explain.
(d) Are the event 'payment by cash' and 'purchase of under $20' independent? Explain.