Question

Find the sample space for the experiment.

Answer 1

Answer:

S ={(1+1=2), (1+2=3), (1+3=4), (1+4=5), (1+5=6), (1+6=7),

     (2+1=3), (2+2=4),(2+3=5),(2+4=6),(2+5=7),(2+6=8),

     (3+1=4), (3+2=5),(3+3=6),(3+4=7),(3+5=8),(3+6=9),

     (4+1=5), (4+2=6),(4+3=7),(4+4=8),(4+5=9),(4+6=10),

     (5+1=6), (5+2=7),(5+3=8),(5+4=9),(5+5=10),(5+6=11),

     (6+1=7), (6+2=8),(6+3=9),(6+4=10),(6+5=11),(6+6=12)}

Step-by-step explanation:

By definition the sample space of an experiment "is the set of all possible outcomes or results of that experiment".

For the case described here: "Toss a six-sided die twice and record the sum of the results".

Assuming that we have a six sided die with possible values {1,2,3,4,5,6}

The sampling space denoted by S and is given by:

S ={(1+1=2), (1+2=3), (1+3=4), (1+4=5), (1+5=6), (1+6=7),

     (2+1=3), (2+2=4),(2+3=5),(2+4=6),(2+5=7),(2+6=8),

     (3+1=4), (3+2=5),(3+3=6),(3+4=7),(3+5=8),(3+6=9),

     (4+1=5), (4+2=6),(4+3=7),(4+4=8),(4+5=9),(4+6=10),

     (5+1=6), (5+2=7),(5+3=8),(5+4=9),(5+5=10),(5+6=11),

     (6+1=7), (6+2=8),(6+3=9),(6+4=10),(6+5=11),(6+6=12)}

The possible values for the sum are 2,3,4,5,6,7,8,9,10,11,12