Question

two dice are rolled. what is the probability p(sum is 6)?
\\(\frac{11}{12}\\)
\\(\frac{5}{36}\\)
\\(\frac{2}{9}\\)
\\(\frac{1}{6}\\)

Explanation:

Step1: Find total number of outcomes

When two dice are rolled, each die has 6 possible outcomes. So the total number of outcomes is \(6\times6 = 36\) since the rolls are independent events.

Step2: Find favorable outcomes

The pairs of numbers on the two - dice that sum to 6 are \((1,5)\), \((2,4)\), \((3,3)\), \((4,2)\), \((5,1)\). There are 5 such pairs.

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 \(P(\text{sum is }6)=\frac{5}{36}\).

Answer:

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