Question

Use the sample space for the total number of possible outcomes when a pair of dice is tossed to find the probability of obtaining a sum of 7 on a single toss of a pair of dice.

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 of $7$ are

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

Number of favorable outcomes = $6$

Hence, the probability of obtaining a sum of 7 on a single toss of a pair of dice = $\frac{6}{36}=\frac{1}{6}$