According to the DSM-5, a standardized classification of mental disorders used by mental health professionals, the following are some, though not all of the criteria used to diagnose Major Depressive Disorder (MDD).

Next to each of the items, I have included a percentage value that is a (fictionalized) representation the approximate percentage of people in the population at large (i.e. all people in the United States - not just people with MDD) who report these symptoms.

Note: Again, please understand that the values reported in this example are made up -- they are not intended to represent real world values.

• Depressed mood: 35.3%
• Anhedonia (loss of interest or pleasure): 8.5%
• Significant weight changes (loss or gain): 45.9%
• Insomnia or Hypersomnia (little or excessive sleep): 49.1%
• Suicidal ideation (thoughts of suicide): 7.8%
• Decreased concentration: not specified
• There are a few others as well

In order to formally diagnose MDD, clinicians will do a thorough history of the patient and combine some of these probabilities. Let's look at a few of these now. For purposes of the probability calculations, you may assume that the symptoms are independent of each other.

1. It is clear that "significant weight change" is quite common. If you see 3 patients in a single morning, what is the probability that all three of them will report this symptom?
2. If you see three patients in a single morning, what is the probability that at least one of them will report significant weight changes?
3. What is the probability that all three of the patients will report decreased concentration?
4. In order to answer the previous questions, you were told to assume that the symptoms are independent of each other. Is this a reasonable assumption? Explain.