Question
Ken wants to buy a video game console. His friend estimates there is a 55% chance he will buy Console A, a 25% chance he will buy Console B and a 20% chance he will buy Console C. Each of the consoles has improved since they were first released but all still have some issues with becoming defective within a year. Console A has a 10% chance of becoming defective, Console B has a 5% chance of becoming defective and Console C has a 1% chance of becoming defective. Draw a tree diagram to represent this situation
Ask by Malone Rojas.
Aug 03,2023 19:00
UpStudy AI Solution
Tutor-Verified Answer
Answer
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├── Console A (0.55)
│ ├── Defective (0.10)
│ │ └── Probability: 0.55 * 0.10 = 0.055
│ └── Not defective (0.90)
│ └── Probability: 0.55 * 0.90 = 0.495
├── Console B (0.25)
│ ├── Defective (0.05)
│ │ └── Probability: 0.25 * 0.05 = 0.0125
│ └── Not defective (0.95)
│ └── Probability: 0.25 * 0.95 = 0.2375
└── Console C (0.20)
├── Defective (0.01)
│ └── Probability: 0.20 * 0.01 = 0.002
└── Not defective (0.99)
└── Probability: 0.20 * 0.99 = 0.198
Solution
Here’s the tree diagram representing the situation with the probabilities:
Choices of Console: Console A 55%, Console B 25%, Console C 20%
Defective within a year: Console A 10%, Console B 5%, Console C 1%
Answered by UpStudy AI and reviewed by a Professional Tutor
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What is the probability that Ken will buy Console A and it will not become defective within a year?
The probability that Ken will buy Console A is 55% and the probability that it will not become defective within a year is 90% (since it has a 10% chance of becoming defective). Therefore, the probability that Ken will buy Console A and it will not become defective within a year is: 0.55 * 0.9 = 0.495
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