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Answer:
There is a 2% probability that the student is proficient in neither reading nor mathematics.
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a student is proficient in reading
B is the probability that a student is proficient in mathematics.
C is the probability that a student is proficient in neither reading nor mathematics.
We have that:
In which a is the probability that a student is proficient in reading but not mathematics and is the probability that a student is proficient in both reading and mathematics.
By the same logic, we have that:
Either a student in proficient in at least one of reading or mathematics, or a student is proficient in neither of those. The sum of the probabilities of these events is decimal 1. So
In which
65% were found to be proficient in both reading and mathematics.
This means that
78% were found to be proficient in mathematics
This means that
85% of the students were found to be proficient in reading
This means that
Proficient in at least one:
What is the probability that the student is proficient in neither reading nor mathematics?
There is a 2% probability that the student is proficient in neither reading nor mathematics.