Question

An 8-sided fair dice is rolled twice and the product of the two numbers obtained when the dice is rolled two times is calculated.(a) Draw the possibility diagram of the product of the two numbers appearing on the dice 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

Answer 1

1.) Kindly check attached picture for possibility diagram

(2)

1) 0.125 2)0.963 3.)0.234 4.)0.625 5.)0.656

Explanation:

Probability = required outcome / Total possible outcomes

1) P(product is a prime number)

Appearance of prime numbers = 8 times

P(product is a prime number) = 8/64 = 0.125

2.) P(not a perfect square) = 1 - p(perfect square)

1 - (12/64) = 52/54 = 0.963

3.) P(a multiple of 5) = 15/64 = 0.234

4.)P(less than or equal to 21) = 40/64 = 0.625

5.)P(divisible by 4 or 6) = 42/64 = 0.656