a pair of standard dice are rolled. find the probability of rolling a sum of 9 with these dice. p(d1 + d2 =…

a pair of standard dice are rolled. find the probability of rolling a sum of 9 with these dice. p(d1 + d2 = 9) = ?

a pair of standard dice are rolled. find the probability of rolling a sum of 9 with these dice. p(d1 + d2 = 9) = ?

Answer

Explanation:

Step1: Find total number of outcomes

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

Step2: Find number of favorable outcomes

The pairs of numbers on the two - dice that sum to 9 are: $(3,6)$, $(4,5)$, $(5,4)$, $(6,3)$. So there are 4 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 $P=\frac{4}{36}=\frac{1}{9}$.

Answer:

$\frac{1}{9}$