Question

Use random-variable notation to represent the event. Suppose that two balanced dice are rolled. Let X denote the sum of the two numbers. Use notation to represent the event that the sum of the two numbers is less than 4.

Answer 1

X-33 where X is 36(total outcome)

Explanation:

If two dice are rolled, the total number of sample space generated will be 6×6 = 36 (since one dice has 6faces.)

The total number of possible outcome of the sum of numbers on both rolled die will also be 36.

Since X is denoted by this total outcome, therefore the total possible outcome will be replaced as X instead of 36.

Possible outcome = event that the sum of the two numbers is less than 4.

The possible outcomes are (1,1),(1,2),(2,1) since the sum of each of the sample space is less than 4.

The events that represent sum of numbers less than 4 are (1+1),(1+2),(2+1) which gives 3 possible outcomes

Therefore;

Event of possible outcomes in terms of the X notation will be (X-33) where X is 36.

P (sum of event less than 4) = possible outcomes/total outcome = 3/X