Exercise 1. Note: The following experiment can be modeled as a uniform probabili

Question

Exercise 1. Note: The following experiment can be modeled as a uniform probability on a sample space with under 100 members. You can answer some questions shortcut counting methods, and other by simply listing out members. Show your work. Ten tiles, each with a digit from 0 to 9, are placed in a bag. We choose two from the bag at random. (A) What is the size of the sample space? (B) What is the chance that the 3 tile is chosen? (C) What is the chance that the sum of the tile values is 97 What is the chance shat both tiles are odd numbers?

Explanation / Answer

Number of tiles in the bag: 10

(A)

Since tiles are drawn at once so number of ways of selecting 2 tiles out of 10 is C(10,2) = 45

That is size of sample space is 45.

(B)

There is only one tile with number of 3 so number of ways of selecting the 3 tile and one other tile from rest 9 tiles is

C(1,1)C(9,1) = 9

So the chance of selecting the 3 tile is

9 /45 = 0.20

(C)

Following table shows all possible values of two tiles and corresponding sum:

Out of 45 outcomes, 5 outcomes shows sum 9 so the required probability is

5 /45 = 0.1111

(D)

Out of 45, 10 outcomes shows both odd tiles so the required probability is

10 / 45 = 0.2222

Tile 1 Tile 2 Sum 0 1 1 0 2 2 0 3 3 0 4 4 0 5 5 0 6 6 0 7 7 0 8 8 0 9 9 1 2 3 1 3 4 1 4 5 1 5 6 1 6 7 1 7 8 1 8 9 1 9 10 2 3 5 2 4 6 2 5 7 2 6 8 2 7 9 2 8 10 2 9 11 3 4 7 3 5 8 3 6 9 3 7 10 3 8 11 3 9 12 4 5 9 4 6 10 4 7 11 4 8 12 4 9 13 5 6 11 5 7 12 5 8 13 5 9 14 6 7 13 6 8 14 6 9 15 7 8 15 7 9 16 8 9 17

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