Question

students in mrs. barness class determined the probability that she will check homework on a randomly chosen day is 0.42. 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. the probabilities are displayed in the tree diagram. what is the probability that mrs. barnes does not check homework if the students take a pop quiz? 0.25 0.33 0.67 0.77

Explanation:

Step1: Calculate the probability of pop - quiz

Use the law of total probability. The probability of a pop - quiz \(P(Q)\) is given by:

$$
LATEXBLOCK0
$$

Step2: Calculate the probability of does not check homework and pop - quiz

\(P(\text{does not check}\cap Q)=P(\text{does not check})\times P(Q|\text{does not check})=0.58\times0.9 = 0.522\)

Step3: Use Bayes' theorem

By Bayes' theorem \(P(\text{does not check}|Q)=\frac{P(\text{does not check}\cap Q)}{P(Q)}\)
Substitute the values: \(P(\text{does not check}|Q)=\frac{0.522}{0.774}\approx0.67\)

Answer:

\(0.67\)