We know that in Armando's senior class 91 students out of 100 senior class students went to the prom. Let's calculate the probability that a randomly chosen student went to the prom.
P(went to the prom) = 91/100 = 0.91
We know that two people are randomly chosen from the entire class. We can define the following events.
A — the first person went to the prom
B — the second chosen person went to the prom
These are two independent events, since the outcome of the first event does not affect the probability of the outcome of the second event. We are interested in finding the probability that at least one of them did not go to the prom. This means there are three possible situations.
The first chosen person did not go to the prom.
The second person did not go to the prom.
Both chosen students did not go to the prom.
Notice that the complement of the three events described above is the event that both students went to the prom. Therefore, we will begin by finding P(AandB). Let's recall the rule for finding the probability of independent events.
Probability of Independent Events
If two events A and B are independent, then P(AandB) = P(A) * P(B).
We already know that the probability that a randomly chosen student went to the prom is equal to 0.91. Therefore, we also know that both P(A) and P(B) are equal to 0.91. We are ready to find P(AandB).
P(AandB) = 0.91 * 0.91 = 0.8281
In order to calculate the probability that at least one of the students did not go to the prom, we need to obtain the probability of the complement P( not(A andB)).
P(not(A andB) ) = 1 - P(A andB)
We can substitute 0.8281 for P(AandB) in the above formula and simplify.
