a pair of standard dice are rolled. find the probability of rolling a sum of 6 with these dice. p(d1 + d2 =…

Explanation:

Step1: Find total number of outcomes

Each die has 6 faces. When two dice are rolled, the total number of outcomes is $6\times6 = 36$ by the multiplication - principle.

Step2: Find number of favorable outcomes

The pairs of numbers on the two dice that sum to 6 are: $(1,5)$, $(2,4)$, $(3,3)$, $(4,2)$, $(5,1)$. So there are 5 favorable outcomes.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(D_1 + D_2=6)=\frac{5}{36}$.

Answer:

$\frac{5}{36}$