Question

You are going to roll two dice What are the outcomes in the sample space?

A) {1, 2, 3, 4, 5, 6}
B) {2, 4, 6, 8, 10, 12}
C) {1-1, 2-2, 3-3, 4-4, 5-5, 6-6}
D) {1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, 5-6, 6-6}

Answer 1

The Correct option is D {1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, 5-6, 6-6}

S = { ( 1, 1 ), ( 1, 2 ), ( 1, 3 ), ( 1, 4 ), ( 1, 5 ), ( 1, 6 )

( 2, 1 ), ( 2, 2 ), ( 2, 3 ), ( 2, 4 ), ( 2, 5 ), ( 2, 6 )

( 3, 1 ), ( 3, 2 ), ( 3, 3 ), ( 3, 4 ), ( 3, 5 ), ( 3, 6 )

( 4, 1 ), ( 4, 2 ), ( 4, 3 ), ( 4, 4 ), ( 4, 5 ), ( 4, 6 )

( 5, 1 ), ( 5, 2 ), ( 5, 3 ), ( 5, 4 ), ( 5, 5 ), ( 5, 6 )

( 6, 1 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }

Explanation:

Let the experiment be the rolling of two dice.

Sample space:

It is the total number of outcomes when the experiment is performed.

Let 'S' be the Sample space for rolling of two dice.

So when to dice are rolled the total number of outcomes or Sample space is given as,

S = { ( 1, 1 ), ( 1, 2 ), ( 1, 3 ), ( 1, 4 ), ( 1, 5 ), ( 1, 6 )

( 2, 1 ), ( 2, 2 ), ( 2, 3 ), ( 2, 4 ), ( 2, 5 ), ( 2, 6 )

( 3, 1 ), ( 3, 2 ), ( 3, 3 ), ( 3, 4 ), ( 3, 5 ), ( 3, 6 )

( 4, 1 ), ( 4, 2 ), ( 4, 3 ), ( 4, 4 ), ( 4, 5 ), ( 4, 6 )

( 5, 1 ), ( 5, 2 ), ( 5, 3 ), ( 5, 4 ), ( 5, 5 ), ( 5, 6 )

( 6, 1 ), ( 6, 2 ), ( 6, 3 ), ( 6, 4 ), ( 6, 5 ), ( 6, 6 ) }