• Also known as the intersection
• The ‘overlap’ between two groups or events.
• $P(A \text{ and } B) = P(A|B) \times P(B) = P(B|A) \times P(A)$
• It does not matter which event, A or B, ‘occurred’ first: $P(A \text{ and } B)= P(B \text{ and } A)$

• Also known as the union
• Includes all of both groups or events
• $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$
• It does not matter which event, A or B, ‘occurred’ first: $P(A \text{ or } B)= P(B \text{ or } A)$

• Also known as a conditional probability
• Is the odds of one event occurring given that another event has already occurred
• The odds of ‘A’ occurring given that ‘B’ has already occurred: $P(A | B) = \frac{P(A \text{ and } B)}{P(B)}$
• The odds of ‘B’ occurring given that ‘A’ has already occurred: $P(B | A) = \frac{P(A \text{ and } B)}{P(A)}$
• The order of the events, A or B, matters: $P(B | A) \neq P(A | B)$

Example 15.1

Problem Setup: Let P(A) = 0.80, P(B) = 0.70, P(A|B) = 0.25

Questions: Can you solve for the following probabilities? And can you find the issue?

1. P(A and B)
2. P(A or B)
3. P(not A)
4. P(not B)

Solutions: Click here to download the written solutions. Click below to reveal the answers one at a time. Also see the next section for video solutions.

Example 15.2

Problem Setup: Let P(A) = 0.50, P(B) = 0.60, P(A and B) = 0.25

Questions: Can you solve for the following probabilities?

1. P(A | B)
2. P(B | A)
3. P(A or B)
4. P(not B)

Solution: Click here to download the written solutions. Click below to reveal the answers one at a time.  Also see the next section for video solutions.

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