in a class of 50 students, 29 are democrats, 11 are business majors, and 5 of the business majors are democrats. If one student is randomly selected, find the probability of
A. choosing a democrat who is not a business major
B. choosing a student who's neither a democrat nor a business major
What about the remaining 5 students?
25 + 11 + 5 ≠ 50
A. 29/50
B. 5/50 = 1/10
To find the probability, we need to divide the number of favorable outcomes by the total number of possible outcomes.
Given information:
Total number of students in the class = 50
Number of students who are Democrats = 29
Number of students who are Business Majors = 11
Number of Business Majors who are Democrats = 5
A. Probability of choosing a Democrat who is not a Business Major:
To find the number of Democrats who are not Business Majors, we subtract the number of Business Majors who are Democrats from the total number of Democrats.
Number of Democrats who are not Business Majors = Total number of Democrats - Number of Business Majors who are Democrats
= 29 - 5
= 24
The total number of possible outcomes remains the same, which is the total number of students in the class, 50.
Probability = Number of favorable outcomes / Total number of possible outcomes
= Number of Democrats who are not Business Majors / Total number of students
= 24 / 50
= 12 / 25
= 0.48 (or 48%)
Therefore, the probability of choosing a Democrat who is not a Business Major is 0.48 or 48%.
B. Probability of choosing a student who is neither a Democrat nor a Business Major:
To find the number of students who are neither Democrats nor Business Majors, we subtract the number of Democrats from the total number of students, and then subtract the number of Business Majors from that result.
Number of students who are neither Democrats nor Business Majors = Total number of students - Number of Democrats - Number of Business Majors
= 50 - 29 - 11
= 50 - 40
= 10
Probability = Number of favorable outcomes / Total number of possible outcomes
= Number of students who are neither Democrats nor Business Majors / Total number of students
= 10 / 50
= 1 / 5
= 0.2 (or 20%)
Therefore, the probability of choosing a student who is neither a Democrat nor a Business Major is 0.2 or 20%.
To find the probability of selecting a particular outcome, we need to divide the number of favorable outcomes by the total number of possible outcomes.
Let's calculate the probabilities step by step:
A. Choosing a democrat who is not a business major:
There are 29 democrats in the class, but 5 of them are business majors. Therefore, the number of democrats who are not business majors is 29 - 5 = 24. The total number of students who are not business majors can be found by subtracting the number of business majors (11) from the total number of students (50): 50 - 11 = 39.
P(democrat and not business major) = (number of democrats who are not business majors) / (total number of students who are not business majors)
P(democrat and not business major) = 24 / 39
B. Choosing a student who's neither a democrat nor a business major:
The number of students who are neither democrats nor business majors can be found by subtracting the number of democrats (29) and the number of business majors (11) from the total number of students (50): 50 - 29 - 11 = 10.
P(neither democrat nor business major) = (number of students who are neither democrats nor business majors) / (total number of students)
P(neither democrat nor business major) = 10 / 50
To simplify these probabilities:
A. P(democrat and not business major) = 24 / 39 ≈ 0.615
B. P(neither democrat nor business major) = 10 / 50 = 0.2
Hence, the probabilities are approximately:
A. 0.615 or 61.5%
B. 0.2 or 20%