Question

a pair of standard dice are rolled. find the probability of rolling a sum of 2 with these dice. p(d₁ + d₂ = 2) =

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: Determine favorable outcomes

The sum of two dice \(D_1 + D_2=2\) occurs when \(D_1 = 1\) and \(D_2 = 1\). So there is 1 favorable outcome.

Step3: Calculate probability

Using the probability formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), we have \(P=\frac{1}{36}\).

Answer:

\(\frac{1}{36}\)