Question

Consider a pair of ten sided dice. (a) what is the probability of rolling nines for both dice. (b) what is the probability that the sum of the dice is 18?

Answer 1

Solution to a :

Probability of rolling 9 and 9:

$$P(x=9 and x=9)= p(x=9) * P(x=9)$$

And

$$P(x=9) = {1 \over 10}$$

Therefore ;

$$= ({1 \over 10})({1 \over 10}) = { 1 \over 100}$$

Answer: 0.01

Solution to b

Probability sum is 18:

$$=P(9 and 9) or P(10 and 8) or P(8 and 10)$$

$= P(x=9) * P(x=9) +$

$$P(x=10) * P(x=8) + P(x=8)*P (x=10)$$

$$= ( {1 \over 10})( {1 \over 10}) + ({1 \over 10}) ({1 \over 10}) + ( {1 \over 10})( {1 \over 10})$$

$$={1 \over 100} + {1 \over 100} + {1 \over 100} = {3 \over 100}$$

Answer: 0.03