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Now, it’s time to apply these concepts to calculate probabilities.

Let’s go back to one of our first examples: event A is rolling an odd number on a six-sided die and event B is rolling a number greater than two. What if we want to find the probability of one or both events occurring? This is the probability of the union of A and B:

$P(A \text{ or } B)$

We can visualize this calculation as follows:

This animation gives a visual representation of the addition rule formula, which is:

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

We subtract the intersection of events A and B because it is included twice in the addition of P(A) and P(B).

What if the events are mutually exclusive? On a single die roll, if event A is that the roll is less than or equal to 2 and event B is that the roll is greater than or equal to 5, then events A and B cannot both happen.

For mutually exclusive events, the addition rule formula is:

$P(A \text{ or } B) = P(A) + P(B)$

This is because the intersection is empty, so we don’t need to remove any overlap between the two events.

### Instructions

1.

In script.py, there is some code written out for you. First, there is a function, prob_a_or_b() which calculates the addition rule. It takes in three arguments:

• a: an event with possible outcomes represented as a set
• b: an event with possible outcomes represented as a set
• all_possible_outcomes: a set that represents all possible outcomes of a sample space

In prob_a_or_b(), the probability of a and b as well as the probabilty of their intersection has been calculated in the following variables:

• prob_a
• prob_b
• prob_inter

Using these variables, write a return statement that returns the probability of events a or b occurring.

2.

In script.py, there are three different random events outlined through sets. The first one is below the following comment:

# rolling a die once and getting an even number or an odd number

Call prob_a_or_b() using the following variables:

• evens
• odds
• all_possible_rolls

Be sure to wrap your function call in a print() statement. Add your line of code below the following comment:

# call function here first

Bonus: Try to calculate the probability using pencil and paper and compare it to the value you get using prob_a_or_b().

3.

The second random scenario is below the following comment:

# rolling a die once and getting an odd number or a number greater than 2

Call prob_a_or_b() using the following variables:

• odds
• greater_than_two
• all_possible_rolls

Be sure to wrap your function call in a print() statement. Add your line of code below the following comment:

# call function here second

Bonus: Try to calculate the probability using pencil and paper and compare it to the value you get using prob_a_or_b().

4.

The final random scenario is below the following comment:

# selecting a diamond card or a face card from a standard deck of cards

Call prob_a_or_b() using the following variables:

• diamond_cards
• face_cards
• all_possible_cards

Be sure to wrap your function call in a print() statement. Add your line of code below the following comment:

# call function here third

Bonus: Try to calculate the probability using pencil and paper and compare it to the value you get using prob_a_or_b().