Question

p (sum of 8)=0.14
correct answer
p (sum of 8)=\frac{5}{36}
part: 1 / 4
part 2 of 4
(b) a sum of 6 or 10
p (sum of 6 or 10)=

Explanation:

Step1: Find number of ways to get sum of 6

When rolling two - dice, the possible pairs for a sum of 6 are (1,5), (2,4), (3,3), (4,2), (5,1), so there are 5 ways.

Step2: Find number of ways to get sum of 10

The possible pairs for a sum of 10 are (4,6), (5,5), (6,4), so there are 3 ways.

Step3: Calculate total number of outcomes when rolling two dice

The total number of outcomes when rolling two dice is $n(S)=6\times6 = 36$.

Step4: Use the addition - rule for mutually - exclusive events

Since getting a sum of 6 and getting a sum of 10 are mutually - exclusive events, $P(\text{sum of }6\text{ or }10)=P(\text{sum of }6)+P(\text{sum of }10)$.
$P(\text{sum of }6)=\frac{5}{36}$ and $P(\text{sum of }10)=\frac{3}{36}$.
So $P(\text{sum of }6\text{ or }10)=\frac{5 + 3}{36}=\frac{8}{36}=\frac{2}{9}$.

Answer:

$\frac{2}{9}$