Question

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.) (a) odd and doubles (b) odd or doubles

Answer 1

SOLUTION:

From given data,

The probability that the sum is as stated when a pair of dice is rolled.

(a) odd and doubles:

Let the sum of odd is denoted by E

the sum of doubles is denoted by F

Then, the event of sum of odd and sum of doubles is denoted by E F

So, number of event of sum of odd is:

n(E) = 18

And, number of event of sum of double is

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

n (F) = 6

we know that number of event of sum of odd and sum of doubles is n(E F) = 0

Total outcome of an experiment is n(s) = 36

Therefore, probability of sum of odd and sum of doubles is:

p(E F) = n(E F) / n(s)

= 0 / 36

(b) odd or doubles

Let the sum of odd is denoted by E

the sum of doubles is denoted by F

Then, the event of sum of odd and sum of doubles is denoted by E F

So, number of event of sum of odd is:

n(E) = 18

And, number of event of sum of double is

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

n (F) = 6

we know that number of event of sum of odd and sum of doubles is n(E F) = 0

And , number of event of sum of odd or sum of doubles is

n(E F) = n(E)+n(F)-n(E F)

= 18+6-0

= 24

Total outcome of an experiment is n(s) = 36

Therefore, probability of sum of odd and sum of doubles is:

p(E F) = n(E F) / n(s)

= 24 / 36

= 3 / 4