a pair of standard dice are rolled. find the probability of rolling a sum of 7 with these dice. p(d1 + d2 =…

a pair of standard dice are rolled. find the probability of rolling a sum of 7 with these dice. p(d1 + d2 = 7) = ?

a pair of standard dice are rolled. find the probability of rolling a sum of 7 with these dice. p(d1 + d2 = 7) = ?

Answer

Explanation:

Step1: Find total number of outcomes

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

Step2: Find number of favorable outcomes

The pairs of numbers on the two dice that sum to 7 are: $(1,6)$, $(2,5)$, $(3,4)$, $(4,3)$, $(5,2)$, $(6,1)$. So there are 6 favorable outcomes.

Step3: Calculate the 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 $P=\frac{6}{36}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$