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:
We can visualize this calculation as follows:
This animation gives a visual representation of the addition rule formula, which is:
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:
This is because the intersection is empty, so we don’t need to remove any overlap between the two events.
Instructions
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 setb
: an event with possible outcomes represented as a setall_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.
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()
.
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()
.
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()
.