Question

students in mrs. barness class determined the probability that she will check homework on a randomly chosen day is 0.8. they also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9. what is the probability that the students will have their homework checked and take a pop quiz on a randomly chosen day? 0.48 0.54 0.72 0.80

Explanation:

Step1: Identify the relevant probabilities

Let \(P(\text{check homework}) = 0.8\) and \(P(\text{pop quiz}|\text{check homework})=0.6\)

Step2: Use the formula for conditional probability \(P(A\cap B)=P(A)\times P(B|A)\)

Here \(A\) is the event of checking homework and \(B\) is the event of having a pop - quiz.
We want to find \(P(\text{check homework}\cap\text{pop quiz})\)
Using the formula \(P(\text{check homework}\cap\text{pop quiz})=P(\text{check homework})\times P(\text{pop quiz}|\text{check homework})\)
Substitute the values: \(P = 0.8\times0.6\)

Step3: Calculate the product

\(0.8\times0.6=\frac{8}{10}\times\frac{6}{10}=\frac{48}{100} = 0.48\)

Answer:

0.48