Answer:
The probability that either Alex or Bryan get an A is 0.9
Step-by-step explanation:
Before we proceed to answer, we shall be making some important notation;
Let A = event of Alex getting an A
Let B = event of Bryan getting an A
From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1
We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)
We can use the addition theorem here;
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) .......................(i)
Also,
P(A) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) .........................(ii)
We can insert ii into i and we have;
P(A ∪ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(A ∩ B) + P(B) - P(A ∩ B) = P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9
