In a university, 30% of the students major in Business management, 25% major in mathematics and 10% major in both business management and mathematics. A student from this university is selected at random.
A) what is the probability that the student majors in business management or mathematics?
B) what is the probability that the student majors in neither of these two courses?
ok, if no dual majors:
a. Pr(BMorM)=.30+.25
b. Pr(neigher)=1-Pr(BMorM)
To find the probability in both of these scenarios, we need to use the concept of probability and set theory. Let's break down each part step by step.
A) Probability that the student majors in business management or mathematics:
To find this probability, we need to add the probability of majoring in business management to the probability of majoring in mathematics and then subtract the probability of majoring in both.
Let's represent the events:
A = Majoring in Business Management
B = Majoring in Mathematics
Given:
P(A) = 30% = 0.30
P(B) = 25% = 0.25
P(A ∩ B) = 10% = 0.10
Using the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Plugging in the values:
P(A ∪ B) = 0.30 + 0.25 - 0.10
P(A ∪ B) = 0.45
Therefore, the probability that the student majors in business management or mathematics is 0.45 or 45%.
B) Probability that the student majors in neither of these two courses:
To find this probability, we need to subtract the probability of majoring in business management or mathematics from 1 since the sum of all possible outcomes must equal 1.
Let's represent the event:
C = Neither majoring in Business Management nor Mathematics
Using the formula:
P(C) = 1 - P(A ∪ B)
Plugging in the value we calculated earlier:
P(C) = 1 - 0.45
P(C) = 0.55
Therefore, the probability that the student majors in neither business management nor mathematics is 0.55 or 55%.