Question

Two dice were rolled, find the probability that: -

1.     Sum is 7 given that product is 10

2.     Sum is less than 4 given that product is 4

3.     Product is 12 given that sum is 8

4.     Sum is divisible by 2

Answer 1

Sum table

Product table

There are $6 \times 6 = 36$ of outcomes

1. Sum is 7 given that product is 10

$x+y=7 \\ x \times y=10$

x= 2 or 5

y = 5 or 2

There two possible combinations: (2,5) and (5,2)

The probability

$P = \frac{2}{36}= \frac{1}{18}$

2. Sum is less than 4 given that product is 4

There is no possible combination

The probability

P=0

3. Product is 12 given that sum is 8

$x+y=8 \\ x \times y = 12$

x= 2 or 6

y= 6 or 2

There two possible combinations: (2,6) and (6,2)

The probability

$P = \frac{2}{36}= \frac{1}{18}$

4. Sum is divisible by 2

Possible combinations: (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

n=18

The probability

$P = \frac{18}{36}= \frac{1}{2}$