Question

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

Explanation:

Step1: Calculate total number of outcomes

When rolling two dice, each die has 6 possible outcomes. So the total number of outcomes is \(6\times6 = 36\) (by the fundamental counting principle \(n(A\times B)=n(A)\times n(B)\)).

Step2: Find number of favorable outcomes

Let the outcomes of the first die be \(x\) and the second die be \(y\) such that \(x + y=8\), where \(1\leq x\leq6\) and \(1\leq y\leq6\).
The pairs \((x,y)\) that satisfy \(x + y = 8\) are \((2,6)\), \((3,5)\), \((4,4)\), \((5,3)\), \((6,2)\). So there are 5 favorable outcomes.

Step3: Calculate the probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{5}{36}\).

Answer:

\(\frac{5}{36}\)