a pair of standard dice are rolled. find the probability of rolling a sum of 10 with these dice. p(d1 + d2 =…

a pair of standard dice are rolled. find the probability of rolling a sum of 10 with these dice. p(d1 + d2 = 10) = ?

a pair of standard dice are rolled. find the probability of rolling a sum of 10 with these dice. p(d1 + d2 = 10) = ?

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 10 are: $(4,6)$, $(5,5)$, $(6,4)$. So there are 3 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 $P=\frac{3}{36}=\frac{1}{12}$.

Answer:

$\frac{1}{12}$