At a school consists of 62% undergraduate, 55% of the students are males, and 48% of the undergraduate students are male.
a. Determine the probability that a randomly selected student is either male or an undergraduate
b. Illustrate the probabilities using a Venn Diagram
a. (0.62*0.55) + (0.62*(0.55-0.48))= 0.3844 = 38.44%
- thank you so much
a. To determine the probability that a randomly selected student is either male or an undergraduate, we can add the probabilities of being male and being an undergraduate and subtract the overlap (the probability of being a male undergraduate) to avoid double counting.
Probability of being male = 55%
Probability of being an undergraduate = 62%
Probability of being a male undergraduate = 48%
P(male or undergraduate) = P(male) + P(undergraduate) - P(male undergraduate)
= 55% + 62% - 48%
= 69%
Therefore, the probability that a randomly selected student is either male or an undergraduate is 69%.
b. Venn Diagram illustration:
Unfortunately, as a text-based bot, I am unable to provide visual illustrations. However, you can draw a Venn diagram with two overlapping circles. Label one circle "Male" and the other "Undergraduate." Inside the "Male" circle, write the probability of being male (55%). Inside the "Undergraduate" circle, write the probability of being an undergraduate (62%). In the overlapping region of the circles, write the probability of being a male undergraduate (48%).
To determine the probability that a randomly selected student is either male or an undergraduate, we can use the principle of inclusion-exclusion.
a. Probability of being male (P(M)) = 55%
Probability of being an undergraduate (P(U)) = 62%
Probability of being a male undergraduate (P(M ∩ U)) = 48%
Using the principle of inclusion-exclusion, the probability that a randomly selected student is either male or an undergraduate can be calculated as:
P(M ∪ U) = P(M) + P(U) - P(M ∩ U)
P(M ∪ U) = 55% + 62% - 48%
= 69%
Therefore, the probability that a randomly selected student is either male or an undergraduate is 69%.
b. Here is a Venn diagram illustrating the probabilities:
Let's represent male students as the set M, and undergraduate students as the set U.
|---------------------|------------------|
| | |
| M | U |
| | |
|------|--------------|---------|--------|
| | (%) | | (62%) |
| Venn | | |
| Diagram | | |
| | | |
|---------------------|---------|--------|
(55%) (48%)
In the Venn diagram, the intersection (M ∩ U) represents male undergraduate students.
The remaining portion of M (outside the intersection) represents male graduate students.
The remaining portion of U (outside the intersection) represents female undergraduate students.
The region outside both M and U represents female graduate students.
The percentages inside the diagram indicate the proportion of students in each category.
To determine the probability that a randomly selected student is either male or an undergraduate, we need to consider the percentages given for each category and how they overlap.
a. To calculate the probability that a randomly selected student is either male or an undergraduate, we need to add the probabilities of being male and being an undergraduate, and then subtract the probability of being both male and undergraduate.
Let's calculate the probabilities step by step:
1. Probability of being male: The percentage of male students is given as 55%. This means that the probability of selecting a male student randomly is 55%.
2. Probability of being an undergraduate: The percentage of undergraduate students is given as 62%. This means that the probability of selecting an undergraduate student randomly is 62%.
3. Probability of being both male and undergraduate: The percentage of male undergraduate students is given as 48%. This means that the probability of selecting a student who is both male and an undergraduate is 48%.
To calculate the probability that a randomly selected student is either male or an undergraduate, we can use the following formula:
Probability ( A ∪ B ) = Probability ( A ) + Probability ( B ) - Probability ( A ∩ B ),
where A represents the event "being male" and B represents the event "being an undergraduate".
Therefore, the probability that a randomly selected student is either male or an undergraduate is:
Probability ( male or undergraduate ) = Probability ( male ) + Probability ( undergraduate ) - Probability ( male and undergraduate )
= 55% + 62% - 48%.
b. To illustrate the probabilities using a Venn diagram, we can draw two overlapping circles. One circle represents the male students, and the other circle represents the undergraduate students. The area where the two circles overlap represents the students who are both male and undergraduate.
The size of each circle should be proportional to the respective percentages given. In this case, the size of the male circle would represent 55% of the total student population, and the size of the undergraduate circle would represent 62% of the total student population.
The overlapping area represents the male undergraduate students, which is 48% of the total student population. This overlapping area should be included in both the male and undergraduate circles.
By visualizing the Venn diagram, we can see the proportions and relationships between the male and undergraduate students, and understand how they contribute to the overall probability.