Let the sample space be Upper S equals StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 EndSet
.
Suppose the outcomes are equally likely. Compute the probability of the event Eequals
"an
odd
number less than 7
."
The event E consists of the numbers 1, 3, and 5.
Since there are 3 outcomes in event E and 10 outcomes in the sample space S, the probability of event E is given by:
P(E) = Number of outcomes in E / Number of outcomes in S = 3 / 10 = 0.3
Therefore, the probability of the event E, "an odd number less than 7," is 0.3.
To compute the probability of the event E = "an odd number less than 7", we need to find the number of favorable outcomes for event E and divide it by the total number of possible outcomes.
1) Finding the number of favorable outcomes:
The odd numbers less than 7 in the sample space S are {1, 3, 5}.
2) Calculating the total number of possible outcomes:
The sample space S consists of 10 elements: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
3) Determining the probability of event E:
The number of favorable outcomes is 3, and the total number of possible outcomes is 10.
Therefore, the probability of the event E, an odd number less than 7, is:
P(E) = Number of favorable outcomes / Total number of possible outcomes
= 3/10
= 0.3 or 30%
To compute the probability of the event E, which is defined as "an odd number less than 7," we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
First, let's identify the outcomes that satisfy the condition of being an odd number less than 7, within the given sample space:
- Odd numbers less than 7: 1, 3, 5
Therefore, the number of outcomes that satisfy the condition is 3.
Next, we need to determine the total number of possible outcomes in the sample space, which is given as 10.
Now we can calculate the probability of event E by dividing the number of favorable outcomes by the total number of possible outcomes:
P(E) = Number of favorable outcomes / Total number of possible outcomes
P(E) = 3 / 10
Hence, the probability of the event E, an odd number less than 7, is 3/10.