Calculate the conditional probability P(COM 201 | COM 101), given P(COM 101 and COM 201) = 0.0125 and P(COM…

Question

Calculate the conditional probability P(COM 201 | COM 101), given P(COM 101 and COM 201) = 0.0125 and P(COM 101) = 0.125.

ScanSolve AI Tutor · Accepted Answer

This problem requires calculating a conditional probability.

Let $C_{101}$ be the event that a student takes COM 101.
Let $C_{201}$ be the event that a student takes COM 201.

We are given:

The probability that a student takes COM 101 and COM 201 in the same semester: $P(C_{101} \text{ and } C_{201}) = 0.0125$ .
The probability that a student takes COM 101: $P(C_{101}) = 0.125$ .

We need to find the probability that a student is taking COM 201, given that he or she is taking COM 101. This is written as $P(C_{201} | C_{101})$ .

The formula for conditional probability is:

P(A|B) = \frac{P(A \text{ and } B)}{P(B)}

Identify the given probabilities.
$P(C_{201} \text{ and } C_{101}) = 0.0125$ $P(C_{101}) = 0.125$
Apply the conditional probability formula.
$P(C_{201} | C_{101}) = \frac{P(C_{201} \text{ and } C_{101})}{P(C_{101})}$ $P(C_{201} | C_{101}) = \frac{0.0125}{0.125}$
Calculate the result.
$P(C_{201} | C_{101}) = 0.1$
Comparing this result with the given options:

a) 0.1

b) 0.1125

c) 0.0016

d) 0.1375

e) 0.4800

The calculated probability matches option (a).

The final answer is $\boxed{\text{a) } 0.1}$ .

Calculate the conditional probability P(COM 201 | COM 101), given P(COM 101 and COM 201) = 0.0125 and P(COM 101) = 0.125.