HELP! 30 POINTS! Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw (
b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square
iii) A multiple of 5
iv) Less than or equal to 21
v) Divisible by 4 or 6

i) 12.5%       ii) 87.5%        iii) 23.4%

Step-by-step explanation:

There are two die, each with 8 sides so the total number of outcomes is 8²

i) Product is a prime number --> 2, 3, 5, 7

Since it is a prime we only have the option of one die being a 1 and the other being the prime number.

So possible successful outcomes is: (1, 2), (1, 3), (1, 5), (1, 7), (7, 1), (5, 1), (3, 1), and (2, 1) = 8 options.

ii) Not a perfect square.  Let's find the probability that it IS a perfect square and subtract that value from the total (64).

Product IS a perfect square --> 1, 4, 9, 16, 25, 36, 49, 64

Possible successful outcomes of a perfect square: (1, 1) (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8) = 8 options.

Product is NOT a perfect square = 64 - 8 = 56 options

iii) Product is a multiple of 5 --> 5, 10, 15, 20, ,25, 30, 35, 40,

Possible successful outcomes of a multiple of 5: (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (7,5), (8, 5), (5, 8), (5, 7), (5, 6), (5, 4), (5, 3), (5, 2), (5, 1) = 15 options

You are limited to 3 questions on so hopefully you can follow what I did to answer the last two questions (less than or equal to 21) and (divisible by 4 or 6). If not, please post this question again and state "Need iv and v only".