Answer:
(a)See below
(b)I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625
Step-by-step explanation:
When an 8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.
The sample space is:
![[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]](https://tex.z-dn.net/?f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
<u>PART A</u>
The sample space of the product a*b of each pair forms the required possibility diagram.
This is given as:

<u>PART B</u>
I) A prime number
The number of products that gives prime numbers = 8
The probability that the product is a prime number

ii) Not a perfect square
Number of products that results in perfect squares =11
The probability that the product is not a perfect square

iii) A multiple of 5
Number of products that are multiples of 5=15
The probability that the product is a multiple of 5

iv) Less than or equal to 21
Number of products which are less than or equal to 21=40
The probability that the product less than or equal to 21

v) Divisible by 4 or 6
Number of products divisible by 4 or 6= 42
The probability that the product is divisible by 4 or 6
