In a class of 48 student 30 offer physics 27 offer biology.
Each of the student offer at least the two subject
What is the probability at random offered
A. Only biology
B. Both physics and biology
C. Physics
To solve this problem, we can use the concept of probability.
Total number of students = 48
Number of students offering physics = 30
Number of students offering biology = 27
A. Probability of only biology = Number of students offering only biology / Total number of students
Since all students offer at least two subjects,
Number of students offering only biology = Total number of students - Number of students offering both physics and biology = 48 - (30 + 27) = 48 - 57 = 0
Therefore, the probability of only biology = 0/48 = 0
B. Probability of both physics and biology = Number of students offering both physics and biology / Total number of students
Number of students offering both physics and biology = 30 + 27 - Total number of students = 30 + 27 - 48 = 9
Therefore, the probability of both physics and biology = 9/48 = 3/16
C. Probability of physics = Number of students offering physics / Total number of students
Therefore, the probability of physics = 30/48 = 5/8
To find the probabilities, we need to first calculate the number of students who fall into each category.
We know that there are 48 students in total, 30 of whom offer Physics and 27 offer Biology. Additionally, we know that each student offers at least these two subjects.
A. To find the probability of a student offering only Biology, we need to subtract the number of students offering both subjects from the total number of students offering Biology. The calculation is as follows:
Number of students offering only Biology = Total number of students offering Biology - Number of students offering both Physics and Biology
Number of students offering only Biology = 27 - 30 (since each student offers both Physics and Biology)
Number of students offering only Biology = 0
Therefore, the probability of a student offering only Biology is 0.
B. To find the probability of a student offering both Physics and Biology, we can use the number of students who offer both subjects:
Number of students offering both Physics and Biology = 30
Therefore, the probability of a student offering both Physics and Biology is:
Probability of offering both Physics and Biology = Number of students offering both Physics and Biology / Total number of students
Probability of offering both Physics and Biology = 30 / 48
Probability of offering both Physics and Biology = 0.625
C. To find the probability of a student offering Physics, we need to subtract the number of students offering both subjects from the total number of students offering Physics:
Number of students offering only Physics = Total number of students offering Physics - Number of students offering both Physics and Biology
Number of students offering only Physics = 30 - 30 (since each student offers both Physics and Biology)
Number of students offering only Physics = 0
Therefore, the probability of a student offering only Physics is 0.
To summarize:
A. Probability of offering only Biology: 0
B. Probability of offering both Physics and Biology: 0.625
C. Probability of offering only Physics: 0