Respuesta :
A) The probability that at least one of the two students will be in class on a given day is; 0.92
B) If at least one of the two students is in class on a given day, the probability that a is in class that day is; 0.8696
How to solve Conditional Probability?
In probability theory, the occurrence of the events may depend on its relative events which are called dependent events while the events not dependent on their relative events are referred to as independent events. For dependent events, if conditional probabilities are required , we will make use of the Baye's Theorem and the total probability theorem sometimes.
We are given;
Probability that student A attends class = 80% = 0.8
Probability that student B attends class = 60% = 0.6
A) The probability that at least one of the two students will be in class on a given day is;
P = 1 - Probability that that neither show up to class on any given day.
P(A ∪ B) = 1 - P(A∼ ∩ B∼)
Where P(A∼ ∩ B∼) = (1 - 0.8) × (1 - 0.6)
P(A∼ ∩ B∼) = 0.08
Thus;
P(A ∪ B) = 1 - 0.08
P(A ∪ B) = 0.92
B) We want to find the probability that student A was in the class given that at least one of them was in the class.
This is obviously a case of conditional probability which will give us the formula;
P(A|A ∪ B) = P(A ∩ (A ∪ B))/P(A ∪ B)
= P(A)/P(A ∪ B)
= 0.8/0.92
= 0.8696
Read more about Conditional Probability at; https://brainly.com/question/10739997
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