Question

Two dice are thrown together. Find the probability that a sum greater than $10$ or a sum less than $5$ turn up

Answer 1

Sample space for total number of possible outcomes

$(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),$

$(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),$

$(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),$

$(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),$

$(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),$

$(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)$

Total number of outcomes $=36$

Favorable outcomes for sum greater than 10 are

$(5,6),(6,5),(6,6)$

Number of favorable outcomes $=3$

Favorable outcomes for sum less than $5$ are

$(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)$

Number of favorable outcomes $=6$

Hence, the probability of obtaining a sum greater than 10 or sum less than 5 = $\frac{3+6}{36}=\frac{1}{4}$