Question

A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.

• A. $\frac{5}{36}$
• B. $\frac{9}{36}$
• C. $\frac{11}{36}$
• D. $\frac{13}{36}$

Answer 1

The correct option is C $\frac{11}{36}$

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 $8$ or getting an even number on both the dices are

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

Number of favorable outcomes = $11$

The probability of getting a sum of $8$ or getting an even number on both the dices, $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{11}{36}$