Question 3: Consider 10 coloured cups, each with a lid. Each cup has its own col

Question

Question 3: Consider 10 coloured cups, each with a lid. Each cup has its own colour. For example there is exactly 1 blue cup, there is exactly 1 red cup, etc. The matching lid and cup are of the same colour. We separate the lids from the cups and throw the cups and lids into a box. So there are 20 objects in the box.

(a) We ask a robot to choose 2 objects at random from 20 objects in the box. What is the probability that the robot chooses a matching lid and cup, i.e. a cup and lid of the same colour?

(b) We ask a robot to choose 4 objects at random from 20 objects in the box. What is the probability that the robot has chosen no matching lid and cup?

(c) We ask a robot to choose 4 objects at random from 20 objects in the box. What is the probability that the robot has chosen exactly one matching lid and cup?

Explanation / Answer

a)

Probability = 10C2 / 20C2 =0.2368

b)

Probability = 10C4 / 20C4 = 0.0433

c)

Probability = 4C2 * 16C2   / 20C4 = 0.1486

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