Question

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 either French or Spanish (or possibly both) is

Answer 1

Answer:

80%.

Step-by-step explanation:

Given the following probabilities:

• P(Micheal Being admitted to French), P(F)=50%
• P(Micheal Being admitted to Spanish), P(S)=50%

In Probability Theory, when we have BOTH , we mean the intersection of the probabilities. Therefore:

• P(Micheal Being admitted to BOTH French and Spanish), $P(F \cap S)=20\%$

We want to determine the probability that he will be enrolled in either French or Spanish (or possibly both).

Probability of either A OR B =$P(F \cup S)$

From Probability Theory:

$P(F \cup S) = P(F)+P(S)-P(F \cap S)\\P(F \cup S) =50+50-20\\P(F \cup S) =80$

The probability that he will be enrolled in either French or Spanish (or possibly both) is 80%.