The sample space is a set of all possible outcomes for an event. A sample space can be small, such as the 2 outcomes when a coin is flipped. Or a sample space can be large, such as the possible number of Texas Classic automobile license plates.
Identifying the sample space can help us to calculate the probability of an event.
The formula given below can be used to find probability of an event.
Example 1 :
What is the probability of rolling an even number on a standard number cube ?
Solution :
Step 1 :
Find the sample space for a standard number cube.
There are 6 possible outcomes.
S = {1, 2, 3, 4, 5, 6}
Step 2 :
Find the number of ways to roll an even number.
The event can occur 3 ways.
{2, 4, 6}
Step 3 :
Find the probability of rolling an even number.
Substitute values and simplify.
P(even) = 3/6
P(even) = 1/2
The probability of rolling an even number is 1/2.
Example 2 :
What is the probability picking a purple marble from a jar with 10 green and 10 purple marbles.
Solution :
Step 1 :
Find the sample space for a standard number cube.
There are 20 possible outcomes.
10 Green marbles and 10 Purple marbles
Step 2 :
Find the number of ways to pick a purple marble.
The event can occur in 10 ways.
Because we have ten purple marbles.
Step 3 :
Find the probability of picking a purple marble.
P (purple) = No. of purple marbles / Total no. of marbles
Substitute values and simplify.
P (purple) = 10 / 20
P (purple) = 1/2
The probability of picking a purple marble is 1/2.
Example 3 :
What is the probability of rolling a number greater than 4 on a standard number cube ?
Solution :
Step 1 :
Find the sample space for a standard number cube.
There are 6 possible outcomes.
S = {1, 2, 3, 4, 5, 6}
Step 2 :
Find the number of ways to roll a number greater than 4.
The event can occur 2 ways.
{5, 6}
Step 3 :
Find the probability of rolling a number greater than 4.
P ( > 4 ) = No. of numbers > 4 / Total no. of numbers
Substitute values and simplify.
P ( > 4 ) = 2 / 6
P ( > 4 ) = 1/3
The probability of rolling a number greater than 4 is 1/3.
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