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 checks 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 the sum of the probability of a pop - quiz when homework is checked and the probability of a pop - quiz when homework is not checked.

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Step2: Calculate the conditional probability

The conditional probability formula is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). Here, \(A\) is "checks homework" and \(B\) is "pop - quiz". \(P(A\cap B)=0.42\times0.6 = 0.252\) and \(P(B) = 0.774\)

$$ P(\text{checks homework}|\text{pop - quiz})=\frac{0.42\times0.6}{(0.42\times0.6)+(0.58\times0.9)}=\frac{0.252}{0.774}\approx0.33 $$

Answer:

\(0.33\)