A shopping mall is having a seasonal lucky draw. For every purchase over S500, a

Question

A shopping mall is having a seasonal lucky draw. For every purchase over S500, a customer can enter the lucky draw once. In the lucky draw, the customer draws a ball from a box containing 80 balls in comprising four different colours. Each colour represents a prize, as shown below Colour Number of balls Prize In the box Red Blue Yellow White 10 28 40 A gold coin $100 cash coupon $50 cash coupon $20 cash coupon If the purchase is over $1000, the customer can draw two balls without replacement. a. Ifa ball is drawn at random, find the probability of getting a cash coupon. b. If two balls are randomly drawn without replacement, find the probability of getting i. ii. iii. One cash coupon and one gold coin. Two cash coupons with the same value It is given that the two cash coupons have the same value; find the probability that the two cash coupons are worth $20 (12) c. It is given that Joe spent S600 on a purchase and got a cash coupon in the lucky dravw Find the probability that he got a S50 cash coupon. d. Mrs Chan is planning to go shopping at the shopping mall. The probability that she will purchase over $1000 is 0.1, and the probability that she will purchase over S500, but not more than $1000 is 0.3 Find the probability that Mrs Chan will get at least one $100 cash coupon.

Explanation / Answer

Solution

(a) P(cash coupon) = 78 balls have cash coupon prize and 2 balls are drwan without replcement

P(cash coupon) = (78/80)*(77/79) = 0.9503

(b) (1) P(One cash coupon and one gold coin) = (78/80)*(2/79) + (2/80)*(78/79) = 0.0494

(II) P(2 cash coupons with same value ) = P(100)+P(50)+P(20)

= (10/80)(9/79) + (28/80)(27/79) + (40/80)(39/79) = 0.3807

(III)P(cash coupon wirth 20 dollars given that coupons are of same value) = ((40/80)(39/79))/0.3807 = 0.6484

(c) P(50 cash coupon given that he won a cashcoupon) = (28/80)/((10/80)+(28/80)+(40/80)) = 0.3590

(d) P(atleast one 100 dollars cash coupon) = P(1 100 cash coupon)+P(2 100 dollars cash coupon)

= (10/80)*0.3 + (10/80)(9/79)*0.1 = 0.0389

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