Question

4.1 Two dices are thrown and the product of the two numbers is recorded.
4.1.1 What is the probability that the product will be 5?
4.1.2 What is the probability that the product will be at most 6?
4.1.3 What is the probability that the product will be at least 7?
4.1.4 What is the probability that the product will be a square number?

Answer 1

Product table

Total number of outcomes = 36

1. A = the product will be 5

A ={(1,5), (5,1)}

n(A)=2

$P(A) = \frac{2}{36}= \frac{1}{18}$

2. B= the product will be at most 6

B= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1), (5,1), (6,1)}

n(B) = 14

$P(B) = \frac{14}{36} = \frac{7}{18}$

3. C= the product will be at least 7

C={(2,4), (2,5), (2,6),

(3,3), (3,4), (3,5), (3,6),

(4,2), (4,3), (4,4), (4,5), (4,6),

(5,2), (5,3), (5,4), (5,5), (5,6),

(6,2), (6,3), (6,4), (6,5), (6,6)}

n(C) = 22

$P(C) = \frac{22}{36} = \frac{11}{18}$

4. D= the product will be a square number

D={(1,1), (1,4), (2,2), (3,3), (4,1), (4,4), (5,5), (6,6)}

n(D) = 8

$P(D) = \frac{8}{36}= \frac{2}{9}$