El Cajon has two ambulance services; the city service and the police service. in an emergency, the probability that the city's service responds is 0.7, the probability the police's service responds is 0.6, while the probability that the city or the police service will respond is 0.9. find the probability that both services will respond to an emergency.
explain please!
2007-05-14 15:21:42 · 1 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
P(A and B) + P(A or B) = P(A) + P(B)
P(A and B) + 0.9 = 0.7 + 0.6
P(A and B) = 0.4
To check out, see if the numbers work out: If there's 0.4 when both services respond, and the city service responds 0.7 of the time, there must be (0.7 - 0.4 = 0.3) of the time when ONLY the city responds. And there must be (0.6 - 0.4 = 0.2) when ONLY the police respond. 1.0 - 0.4 - 0.3 - 0.2 = 0.1 (nobody responds), so it works.
2007-05-14 15:27:37 · answer #1 · answered by McFate 7 · 0⤊ 0⤋