From the provided image, we have a tree diagram showing the distribution of men passing or failing a test. Here's how to solve the problem step by step.

Problem

We need to find the probability that a man chosen at random failed his test.

Steps:

1. Understand the Tree Diagram:
   • At the top, there are 60 men in total.
   • These men are split into two categories:
     • 39 passed the test.
     • 21 failed the test.
   • The 39 who passed:
     • 27 men were "male" who passed.
     • 12 men "failed" despite being categorized initially as passers.
   • The 15 %, remained test break down

datIt seems there was a mistake in my response earlier. Let me analyze the problem properly and continue. The tree diagram provided in the image has information about the outcomes of a test for 60 men, categorized into passing and failing. The goal is to calculate the probability of selecting a man at random who failed the test. Here's the analysis:

Information from the Diagram:

1. Total men: 60.
2. 39 men passed:
   • 27 passed directly.
   • 12 failed after being classified under "pass."
3. 21 men failed:
   • 6 passed after being classified under "fail."
   • 15 failed directly.

Total Failures:

To find the total number of failures:

• From the "pass" group: 12 failed.
• From the "fail" group: 15 failed.

Thus, total failures = $12 + 15 = 27$.

Probability of Failing:

The probability that a man chosen at random failed his test is:

$P(\text{failed}) = \frac{\text{Number of failures}}{\text{Total men}} = \frac{27}{60}$

Simplify the fraction:

$P(\text{failed}) = \frac{9}{20} = 0.45$

Final Answer:

The probability that a man chosen at random failed his test is 0.45 (or 45%).

Let me know if you'd like further explanation or details! Here are some related questions for further exploration:

1. What is the probability that a randomly chosen man passed the test?
2. What is the ratio of men who failed to those who passed?
3. If another group of 30 men took the test and 10 failed, what would the new overall probability of failing be?
4. How can the probability of passing directly (from the tree) be calculated?
5. How can this type of problem be visualized without a tree diagram?

Tip: Always add probabilities along branches when calculating total outcomes!