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

B)

1.) 7/64 (2.) 27/32 (3.)15/64 (4.)5/8 (5.)21/32

Step-by-step explanation:

Given the following :

Two 8 - sided fair die (1, 2, 3, 4, 5, 6, 7, 8)

Total sample space = 8^2 = 64

B1)

Probability = (number of required outcome / number of total possible outcomes)

probability of getting a prime number:

number of prime numbers in possibility diagram = 7

1) P(getting a prime number) = 7/64

11) P(not a perfect square)

Not a perfect square values in the diagram = 54

= 54 / 64 = 27 / 32

111) a multiple of 5:

Multiple of 5 in the diagram = 15

= 15 / 64

IV) Less than or equal to 21:

= 40/64 = 5/8

V) divisible by 4 or 6:

Numbers divisible by four or 6 = 42

= 42 / 64 = 21 / 32

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this