Ramon has applied to both Princeton and Stanford. He thinks the probability that Princeton will admit him is 0.4, the probability that Stanford will admit him is 0.5, and the probability that both will admit him is 0.2.
What is your question?
To solve this problem, we can use the concept of conditional probability. Let's represent the events as follows:
A = Admission by Princeton
B = Admission by Stanford
The probability that Ramon will get admitted to both Princeton and Stanford can be written as P(A ∩ B) = 0.2.
The probability that Ramon will get admitted to Princeton, P(A), is given as 0.4.
The probability that Ramon will get admitted to Stanford, P(B), is given as 0.5.
To find the probability that Ramon will get admitted to at least one of the universities, we can use the principle of inclusion-exclusion:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Substituting the given values, we have:
P(A ∪ B) = 0.4 + 0.5 - 0.2
P(A ∪ B) = 0.7
Therefore, the probability that Ramon will get admitted to at least one of the universities (Princeton or Stanford) is 0.7, or 70%.