Question

when two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in the accompanying figure. let y denote the sum of the dice. complete parts (a) through (g) below. a. what are the possible values of the random variable y? y = 2,3,4,5,6,7,8,9,10,11,12 (type whole numbers. use a comma to separate answers as needed.) b. use random - variable notation to represent the event that the sum of the dice is 3. select the correct choice below and fill in the answer box within your choice. a. {y = 3} b. p( ) c. find the probability that the sum of the dice is 3. the probability is (type an integer or a simplified fraction.)

Explanation:

Step1: Identify favorable outcomes

The pairs of dice - values that sum to 3 are (1, 2) and (2, 1). So there are 2 favorable outcomes.

Step2: Calculate probability

The total number of outcomes when two dice are rolled is 36. The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{2}{36}=\frac{1}{18}$.

Answer:

$\frac{1}{18}$