a pair of standard dice are rolled. find the probability of rolling a sum of 8 with these dice. p(d₁ + d₂ =…

a pair of standard dice are rolled. find the probability of rolling a sum of 8 with these dice. p(d₁ + d₂ = 8) = ?

a pair of standard dice are rolled. find the probability of rolling a sum of 8 with these dice. p(d₁ + d₂ = 8) = ?

Answer

Explanation:

Step1: Calculate total number of outcomes

When rolling two dice, each die has 6 possible outcomes. By the multiplication principle, the total number of outcomes is (6\times6 = 36).

Step2: Find number of favorable outcomes

The pairs ((D_1,D_2)) that sum to 8 are ((2,6)), ((3,5)), ((4,4)), ((5,3)), ((6,2)). So there are 5 favorable outcomes.

Step3: Calculate probability

The probability formula is (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). Substituting the values, we get (P=\frac{5}{36}).

Answer:

(\frac{5}{36})