Question

When rolling two six-sided dice, are rolling at least one six and rolling at least one four independent events? Show a calculation that supports your answer.

Answer 1

The sample space of rolling a pair of dice is S= { (1,1), (1,2),(1,3),(1,4),(1,5),(1,6), (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Let A be an event of rolling at least one six.

The favourable points of A are A = {(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Probability of A = P (A) = 11/36

Let B be an event of rolling at least one four.

The favourable points of B are B ={ (1,4),(2,4),(3,4),(4,4),(5,4)(6,4),(4,1),(4,2),(4,3),(4,5),(4,6)}

Then the event of rolling at least one four and at least one six is A intersection B denoted by AB

Probability of A intersection B = P (AB) = P (A)P (B/A)

=( 11/36 )(1/36)= 11/36^2

Hence these two events are not independent. Since P (AB) is not equal to P (A)P (B).

Probability of B = P (B)= 11/36