Question

The prior probability that an entering undergraduate student will get their ba if they have a good high school gpa is given by the answer of the previous question. in addition, 90% of students who graduate with a ba also have a high sat score, whereas 55% of students who drop out have high sat scores.

The probability that an entering freshman who has a good high-school gpa and high sat scores will graduate with a ba is ____ (round to 2 decimal places)

Answer 1

To calculate the probability that an entering freshman with good high school GPA and high SAT scores will graduate with a BA, we need to use conditional probability. Using Bayes' theorem, we can estimate the probability by using the prior probability, the conditional probability of SAT scores given graduation, and the conditional probability of SAT scores given dropout.

Step-by-step explanation:

In order to calculate the probability that an entering freshman who has a good high-school GPA and high SAT scores will graduate with a BA, we need to use conditional probability. Let's use the following notation:

• A: Student graduates with a BA
• HS: Student has a good high school GPA
• SAT: Student has high SAT scores

We are given:

• P(A|HS) = Previous answer (prior probability) = 0.7
• P(SAT|A) = 0.9
• P(SAT|not A) = 0.55

We want to find P(A|HS and SAT). Using Bayes' theorem:

P(A|HS and SAT) = (P(HS and SAT|A) * P(A)) / P(HS and SAT)

Since P(HS and SAT|A) = P(SAT|A) = 0.9:

P(A|HS and SAT) = (0.9 * 0.7) / P(HS and SAT)

To find P(HS and SAT), we can use the law of total probability:

P(HS and SAT) = P(HS and SAT|A) * P(A) + P(HS and SAT|not A) * P(not A)

We don't have all the necessary information to calculate P(HS and SAT|not A) or P(not A), so we cannot find the exact value of P(A|HS and SAT). However, we can use the given values to estimate an approximate answer.