At a High school, 70% of the seniors have taken an advance calculus course. Of those who have taken Advanced Calculus, 60% will apply for a Pre-Health

Kyran Hudson 2020-10-27 Answered
At a High school, 70% of the seniors have taken an advance calculus course. Of those who have taken Advanced Calculus, 60% will apply for a Pre-Health science major when they apply for college admission. Of those who have not taken advanced calculus, 40% will apply for a Pre-Health science major when they apply for college admission. A senior is selected at random. What is the probability that the senior have taken advanced calculus, given that the senior will apply for a pre-health science major?
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Expert Answer

Yusuf Keller
Answered 2020-10-28 Author has 90 answers
Step 1
Given data:
The given percentage of the students that are taken an advanced calculus course is P(A)=70%=0.70.
The given percentage of the students who have taken Advanced calculus and applied for pre-health science is P(AH)=60%P(A).
The given percentage of the students who have not taken Advanced calculus and applied for pre-health science is P(B)=40%(100%-P(A)).
The given percentage of the students who have taken Advanced calculus and applied for pre-health science is,
P(AH)=60%(0.70)=0.42
The given percentage of the students who have not taken Advanced calculus and applied for pre-health science is,
P(B)=40%(1-0.7)=0.12
Step 2
The expression for the probability for the students who are taken pre-health science is, P(H)=P(AH)+P(B)
Substitute the given values in the above expression.
P(H)=0.42+0.12=0.54
The expression for the probability that the senior has taken advanced-calculus given that senior applied for pre-health science is,
P(AH)=P(AH)P(H)
Substitute the above-calculated values in the expression.
P(AH)=0.420.54=0.777
Thus, the probability that the senior has taken advanced-calculus given that the senior applied for pre-health science is 0.777.
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