make a tree diagram for:
two methods A and B are available for teaching a certain industrial skill. the failure rate is 20% for A and 10% for B. however, B is more expensive and is therefore only used 30% of the time (A is used the other 70%). A worker is selected at random, what is the probability that he failed to learn the skill?
To solve this question using a tree diagram, follow these steps:
Step 1: Draw the main branch representing the two teaching methods, A and B.
Step 2: Label each branch with the corresponding method name and write the probability of using that method next to it. In this case, A is used 70% of the time (0.70), and B is used 30% of the time (0.30).
Step 3: From each method branch, create two sub-branches representing the outcomes: "Success" and "Failure." Label each sub-branch accordingly.
Step 4: Write the corresponding failure rates next to the failure branches. Method A has a failure rate of 20% (0.20), and method B has a failure rate of 10% (0.10).
Step 5: Calculate the probability of each outcome by multiplying the probabilities along the branches. For example, the probability of selecting method A and having a successful outcome is 0.70 * (1 - 0.20) = 0.70 * 0.80 = 0.56.
Step 6: Calculate the overall probability of failure by adding up the probabilities of failure from both methods. The probability of failure for method A is 0.70 * 0.20 = 0.14, and the probability of failure for method B is 0.30 * 0.10 = 0.03.
Step 7: Add up the failure probabilities for both methods: 0.14 + 0.03 = 0.17.
Therefore, the probability that a randomly selected worker fails to learn the skill is 0.17 or 17%.