Michael wants to take French or Spanish or both But classes are closed, and he must apply and get accepted to be allowed to enroll in a language class. He has a 50% chance of being admitted to french, a 50% chance of being admitted to Spanish, and a 20% chance of being admitted to both French and Spanish if he applies to both French and Spanish, the probability that he will be enrolled in French or Spanish (or possibly both) is
To find the probability that Michael will be enrolled in French or Spanish (or possibly both), we need to calculate the union of the probabilities of being enrolled in each language.
Let F be the event of being enrolled in French, and S be the event of being enrolled in Spanish. We know that P(F) = 0.5, P(S) = 0.5, and P(F∩S) = 0.2.
The probability of being enrolled in French or Spanish (or possibly both) can be calculated using the formula:
P(F∪S) = P(F) + P(S) - P(F∩S)
P(F∪S) = 0.5 + 0.5 - 0.2
P(F∪S) = 0.8
Therefore, the probability that Michael will be enrolled in French or Spanish (or possibly both) is 0.8 or 80%.
To determine the probability that Michael will be enrolled in French or Spanish (or possibly both), we can use the principle of inclusion-exclusion.
Let's denote:
- Event F: Michael gets admitted to French.
- Event S: Michael gets admitted to Spanish.
We are given the following probabilities:
P(F) = 0.50 (50% chance of being admitted to French)
P(S) = 0.50 (50% chance of being admitted to Spanish)
P(F∩S) = 0.20 (20% chance of being admitted to both French and Spanish)
We want to find P(F∪S), the probability of Michael being enrolled in French or Spanish.
Using the principle of inclusion-exclusion, we can calculate P(F∪S) as follows:
P(F∪S) = P(F) + P(S) - P(F∩S)
P(F∪S) = 0.50 + 0.50 - 0.20
P(F∪S) = 0.80
Therefore, the probability that Michael will be enrolled in French or Spanish (or possibly both) is 0.80 or 80%.