2. Charles Mueller has applied two study abroad programs in summer. One program is in Barcelona of Spain, and another program is in Cancn of Mexico. Charles is told that the chance of studying abroad is lower due to COVID-19 in 2020. So far, there is a 0.25 probability that he will be admitted in the program in Spain and there is a 0.20 probability that he will be admitted in the program in Mexico. There is a 0.35 probability he will be admitted in at least one program this coming summer.

(1) Given that Charles is admitted in the program in Mexico, what is the probability that he will be also admitted in the program in Spain?

(2) Are these two programs independent events? Explain using probabilities.

(3) Are these two programs mutually exclusive? Explain using probabilities.