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 the students will have a pop quiz on a randomly selected day? 0.25 0.52 0.77 0.90

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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 the students will have a pop quiz on a randomly selected day?

0.25
0.52
0.77
0.90
The image is a decision tree diagram that illustrates the probability of different outcomes based on whether homework is checked or not on a random day. The diagram breaks down as follows:

1. **Random Day**: The starting point of the decision tree. 

2. **Homework Check**:
   - Probability of checking homework: **0.42**
     - If homework is checked:
       - Probability of a pop quiz: **0.60**
       - Probability of no pop quiz: **0.40**
   
3. **No Homework Check**:
   - Probability of not checking homework: **0.58**
     - If homework is not checked:
       - Probability of a pop quiz: **0.90**
       - Probability of no pop quiz: **0.10**

Each branch of the tree provides a specific path with associated probabilities leading to the final outcomes of either having a pop quiz or not.
Transcribed Image Text:The image is a decision tree diagram that illustrates the probability of different outcomes based on whether homework is checked or not on a random day. The diagram breaks down as follows: 1. **Random Day**: The starting point of the decision tree. 2. **Homework Check**: - Probability of checking homework: **0.42** - If homework is checked: - Probability of a pop quiz: **0.60** - Probability of no pop quiz: **0.40** 3. **No Homework Check**: - Probability of not checking homework: **0.58** - If homework is not checked: - Probability of a pop quiz: **0.90** - Probability of no pop quiz: **0.10** Each branch of the tree provides a specific path with associated probabilities leading to the final outcomes of either having a pop quiz or not.
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