These 20 discs are in a bag.
11
11
11
11
22
22
22
22
22
22
33
33
33
33
33
33
33
44
44
44
Two of the discs are taken at random from the bag.
Work out the probability that the first disc has a smaller number than the second disc.
[4 marks]

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gavbutler21 gavbutler21 · Answer 1 · 2021-04-03T17:10:27+02:00

2/6 chance of that occurring

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fichoh fichoh · Answer 2 · 2021-11-13T07:36:56+01:00

Using the concept of probability, the probability that the first disk selected has a smaller number than the second is 0.381

Disk marked 11 = 4

Disk marked 22 = 6

Disk marked 33 = 7

Disk marked 44 = 3

Total disks = 20

Recall :

Ways of making selection such that first disk is smaller than second :

First = 11 and second = 22 = (4/20 × 6/19) = 0.0631

First = 11 and second = 33 = (4/20 × 7/19) = 0.0736

First = 11 and second = 44 = (4/20 × 3/19) = 0.0316

First = 22 and second = 33 = (6/20 × 7/19) = 0.1105

First = 22 and second = 44 = (6/20 × 3/19) = 0.0474

First = 33 and second = 44 = (7/20 × 3/19) = 0.0553

Hence,

P(first disk < second) = (0.0631 + 0.0736 + 0.0316 + 0.1105 + 0.0474 + 0.0573) = 0.381

Therefore, probability that the first disk selected is smaller than the second will be 0.381

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