1. 28% of symptomatic COVID-19 patients whose age group is 50 to 60 years are hospitalized. For the age group 65 years and older, the rate is 42%. Mary 55 years old and James 67 years old are husband and wife who have become COVID-19 symptomatic. Assume that the events of hospitalization of individuals are independent from each other and answer the following questions in parts a. and b.

a. What is the probability that at least one of them will be hospitalized?

b. What is the probability that James will be hospitalized, and Mary won't?

2. In a city 30% of the houses and 60% of the condominiums use natural gas for heating. 65% of the residences in the city are houses and the rest are condominiums.

a. If a residence is selected at random from this city, what is the probability it uses natural gas for heating?

b. If a residence uses natural gas for heating, what is the probability it is a condominium