5. In the table below, 400 individuals are classified according to whether or no

Question

5. In the table below, 400 individuals are classified according to whether or not they were vaccinated against influenza and whether or not they were attacked by influenza. Vaccinated 85 190 Not vaccinated 60 65 Attacked Not Attacked If a person is chosen at random, find the probability that: a) the person was vaccinated and attacked b) the person was attacked, given that the person was vaccinated 6·The town of Metroville has two ambulance services: the city service and a citizen's service. In an emergeney, the probability that the city service responds is 0.6, the probability that the citizen's service responds is 0.8, and the probability that either of the services responds is 0.9. Find the probability that both services will respond to an 7. Two fair dice are tossed. Find the probability of observing each of the following events A: The sum of the numbers is equal to 8 B: A 4 appears on at least one of the dice.

Explanation / Answer

5)

The person was vaccinated and attacked:

P(V) =275/400, P(A) =145/400 and P(V | A)= 85/145

P( V and A) = P(V | A) *P(A) = 85 /145 * 145/400= 85/400= 0.2125

b) The person was attacked given that the person was vaccinated:

P(V) =275/400, P(A) =145/400 and P( V and A) = 85/400

P( A | V) = P( A and V) / P(V) = (85/400) / ( 275/400) = 85/275 = 0.309091

Vaccinated Not vaccinated Total Attached 85 60 145 Not attacked 190 65 255 Total 275 125 400

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