Question

Two workshops were offered to math teachers in a local school district. 25% of the math teachers attended the Common Core (CC) workshop, 40% of the math teachers attended the Professional Learning Communities (PLC) workshop, and 10% of the math teachers attended both workshops.

a) What is the probability a teacher attended the PLC workshop given that they attended the CC workshop? Show all work.

b) Are "attended the CC workshop" and "attended the PLC workshop" independent? Explain.

c) What is the probability a teacher did not attend the PLC workshop given that they did not attend the CC workshop? Show all work.

Answer 1

Here we have

P(CC) = 0.25, P(PCL) = 0.40, P(CC and PCL) = 0.10

a)

The probability a teacher attended the PLC workshop given that they attended the CC workshop is

P(PCL | CC) = P(CC and PCL) / P(CC) = 0.10 / 0.25 = 0.40

Answer: 0.40

b)

Yes because

P(PCL | CC) = P(PCL)

Answer: Yes

c)

By the addition rule we have

P(PCL or CC) = P(CC) + P(PCL) - P(CC and PCL) = 0.25 + 0.40 -0.10 = 0.55

By the Demorgan's law we have

P(not PCL and not CC) = 1 - P(PCL or CC) = 1 - 0.55 = 0.45

By the complement rule,

P(not CC) = 1 - P(CC) = 1 - 0.25 = 0.75

So the probability a teacher did not attend the PLC workshop given that they did not attend the CC workshop is

P(not PCL | not CC) = P(not PCL and not CC) / P(not CC) = 0.45 / 0.75 = 0.60

Answer: 0.60