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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
0.10
(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.
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