A department store tabulated the relative frequencies of the amounts of purchase
ID: 3126246 • Letter: A
Question
A department store tabulated the relative frequencies of the amounts of purchases and the method of payment. The results are shown below.
(a) What proportion of purchases are paid for in cash?
(b) Given that a purchase is for more than $100, what is the probability that it is paid for by credit?
(c) Are payment by credit and amount > $100 independent events?
I'm not sure if I'm on the right track.
a) 0.17/1 = 0.17
b) P(purchase>$100 | paid by credit) = [P(pur>$100 AND paid by credit)] / [P(paid by credit)] = 0.23 / 0.47 = 0.4894
c) yes they are independent because P(purchase>$100 | paid by credit) = P(paid by credit)
Cash Credit Debit <$20 0.09 0.03 0.04 $20-$100 0.05 0.21 0.18 >$100 0.03 0.23 0.14Explanation / Answer
A department store tabulated the relative frequencies of the amounts of purchases and the method of payment. The results are shown below.
Cash
Credit
Debit
<$20
0.09
0.03
0.04
0.16
$20-$100
0.05
0.21
0.18
0.44
>$100
0.03
0.23
0.14
0.4
0.17
0.47
0.36
1
(c) Are payment by credit and amount > $100 independent events?
No, they are not independent because P(purchase>$100 | paid by credit) P(paid by credit)
( 0.23/0.47 0.47 )
Cash
Credit
Debit
<$20
0.09
0.03
0.04
0.16
$20-$100
0.05
0.21
0.18
0.44
>$100
0.03
0.23
0.14
0.4
0.17
0.47
0.36
1
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