The JMU health clinic noticed a spike in visits by students

The JMU health clinic noticed a spike in visits by students with u-symptoms. They had 100 students visit in total. Of these, 10 had the normal u, 40 had a type of stomach u, and 50 were completely healthy. They asked each student whether they had eaten at the Swedish restaurant on campus. Overall, 30 students had eaten there, and 13 of those had gotten the stomach u while 2 of those had gotten the normal u. (a) How many students had both the stomach and the normal u? (b) What is the probability of having either type of u if you had eaten at that restaurant? (c) Did going to that restaurant change the risk of contracting dierent us, i.e., are the events of visiting the restaurant and contracting dierent us independent?

Solution

a)accoding to the question we have 100 students

out of which 10 got normal flu and 40 got stomah flu, and 50 were healthy

adding all we get 100

hence there is no person who got both

b)total 30 students had eaten up at swedish restaurant

13 got stomach flu and 2 got normal therefore

probability = 13+2 = 15/30 = 0.5

c)students got flu because they have eaten up there not only visited the the restaurant.

therefore visiting the restaurant not change the risk while which means that both are independent.