Suppose you roll a single fair die and note the number rolle

Suppose you roll a single fair die and note the number rolled.

a. What is the sample space for a single roll of a fair die? Are the outcomes equally likely?

b. Assign probabilities to the outcomes in the sample space found in part (a). Do these probabilities add up to 1? Should they add up to 1? Why?

c. What is the probability of getting a number less than 4 on a single roll?

d. What is the probability of getting a 1 or a 2 on a single roll?

Solution

A sample space is a set of all possible outcomes of a random experiment.

A)    In rolling a fair die the set of all possible outcome or the sample space is = {1,2,3,4,5,6}

Yes, here we can clearly see that all the outcomes are equally likely.

B)   Because all the outcomes are equally likely so the probability to each outcome of the above experiment is 1/6.

There are 6 outcome and each outcome has 1/6 probability so the sum of all the probability = (1/6)*6=1

The sum is 1 because individual outcome makes the whole sample space and the probability of the sample space is always 1.

C)   Favorable condition for getting outcome less than 4 is getting 1 or 2 or 3.

So the probalitity of the above event is=3/6 = 0.5

D)   Favorable condition for getting 1 or 2 is = 2

Total possible output = 6

So, the probability of the given event = 2/6

                                                     = 1/3