Students in Mrs. Barnes’s 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