PL answer this question

Question

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

Answer 1

I can't show the table as it takes too much memory. Have the numbers 1-8 as your first column and first row and show their product as the intersection. In Excel, you can use $signs with the cell reference to do this multiplication across the table.

There are 64 possible outcomes. Thus,

b) i) the first column of products and row 2, 3, 5, and 7 or the first row and columns 2, 3, 5, 7

8 possibilities / 64 = 1/8

ii) Let's count the squares, instead, and subtract form 64.

We have the 8 numbers on the diagonal, (1,4), (4, 1), (2, 8), (8, 2), or 12 numbers, so there are 64 - 12 = 52 nonsquares, and the probability is 52/64 = 13/16

iii) we have everything in the fifth row and fifth column minus (5,5) to avoid counting twice is 2*8 - 1 = 15

15/64

iv) All in the first two rows and the sum for i = 3 to 8 of int(21/i) = 8 + 8 + 7 + 5 + 4 + 3 + 3 + 2 = 40

40/64 = 5/5