Probability question A shopping mall is having a seasonal lucky draw. For every

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Probability 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 ColourNumber of balls Prize In the box Red Blue Yellow White 10 28 40 A gold coin S100 cash coupon $50 cash coupon S20 cash coupon If the purchase is over $1000, the customer can draw two balls without replacemernt If a ball is drawn at random, find the probability of getting a cash coupon If two balls are randomly drawn without replacement, find the probability of getting i. ii. iii. a. b. 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) It is given that Joe spent $600 on a purchase and got a cash coupon in the lucky draw Find the probability that he got a $50 cash coupon c. 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

a. If a ball is drawn at random

Probability of geting a cash coupon = total cash coupon/ total prizess = 78/80 = 0.975

b. (i) One cash coupon and one gold coin.

Pr(One case coupon and one gold coin) = (78/80) * (2/79) + (2/80) * (78/79) = 0.0493

(ii) Two cash coupons with the same value.

so, Pr(Two balls with same value) = Pr(Blue in first chance) * Pr(blue in second chance) + Pr(yellow in first chance) * Pr(yellow ball in second chance) + Pr(White in first chance) * Pr(white in second chance)

= (10/80) * (9/79) + (28/80) * (27/79) + (40/80) * (39/79) = 0.381

(iii) Here two cash coupons are worth $ 20.

so Pr(both cash coupns are $ 20 l Two cash coupons have same value)

= (40/80) * (39/79)/ ((10/80) * (9/79) + (28/80) * (27/79) + (40/80) * (39/79) ) = 0.6484

(c) He get a cash coupon in lucky draw.

Pr( $ 50 cash coupon l Cash coupon) = 28/(40 + 28 + 10) = 0.359

(d) Here If is shopping done by Mrs Chan

Pr(X > $ 1000) = 0.1

Pr($ 500 < X < $ 1000) = 0.3

Pr(X < $ 500) = 0.6

So,

If X > $ 1000 ; then she will get two balls to pick where she can get at max two cash coupon

Pr(Get at least one $ 100 cash coupon) = Pr(Two $ 100 cash coupn) + Pr(one $ 100 cash coupon)

= (10/80) * (9/79) + 2 * (10/80) * (70/79) = 0.2356

if $ 500 < X < $ 1000 then she will get one ball to pick and can get max one cash coupon.

Pr(Get at least one $ 100 coupon) = 10/80 = 1/8 = 0.125

if X > $ 500

then there is no ball to pick

Pr(Get at least one $ 100 coupon) = 0

Pr(Mrs chan will get atleat one $ 100 cashcoupn) = 0 * 0.60 + 0.125 * 0.30 + 0.2356* 0.1 = 0.061

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