Statstic Question?

Question

In a survey taken by an unknown medium last year, 1180 students claimed they voted for reducing the ozone layer in the atmosphere, 2220 claimed the voted for limiting the number of cars circulating around the world during a specific day, and 800 students claimed they voted for reducing the ozone layer in the atmosphere and limiting the number of cars circulating around the world. The Medium questioned 3,100 students last year. If one student is randomly selected,

a) find the probability that he/she voted for reducing the ozone layer in the atmosphere

and reducing the number of cars circulating around the world during a specific day.

b) find the probability that he/she voted for reducing the ozone layer in the atmosphere or reducing the number of cars circulating around the world during a specific day

Answer 1

a) this is given to us in the problem statement

P(ozone AND cars) = 800 / 3100

b)  for any two events A and B

P(A or B) = P(A) + P(B) - P(A and B)

P(ozone OR cars)

= P(ozone) + P(cars) - P(ozone AND cars)

= 1180 / 3100 + 2220 / 3100 - 800 / 3100

= 2600 / 3100

= 0.8387097