Question

half of a class took form a of a test, and half took form b. of the students who took form b, 39% passed. what is the probability that a randomly chosen student took form b and did not pass?
a 0.055
b 0.195
c 0.305
d 0.390

Explanation:

Step1: Calculate the probability of taking Form B

Since half of the class took Form B, the probability of taking Form B, \(P(B)=\frac{1}{2}=0.5\)

Step2: Calculate the probability of not passing Form B

The probability of passing Form B is \(39\% = 0.39\). So the probability of not passing Form B given that a student took Form B, \(P(\text{not pass}|B)=1 - 0.39=0.61\)

Step3: Use the multiplication rule for probability

The multiplication rule for probability is \(P(B\cap\text{not pass})=P(B)\times P(\text{not pass}|B)\)
Substitute \(P(B) = 0.5\) and \(P(\text{not pass}|B)=0.61\) into the formula:
\(P(B\cap\text{not pass})=0.5\times0.61 = 0.305\)

Answer:

C. \(0.305\)