two dice are rolled. what is the probability p(sum is 6)?\n\\(\\frac{11}{12}\\)\n\\(\\frac{5}{36}\\)\n\\(\\fr…

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

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

Answer

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})