Question

5. Suppose E, F, and G are three disjoint events where P(E)- .15, P(F)- .25, and P(G).60. Find the following: (a) P(F or G) (b) P(Ec) (c) P((E or F)c) (d) P(FnG) 6. A new diagnostic test for a disease is studied. It is known whether or not these 100 individuals have the disease and the diagnostic test is administered. The results are as follows infectedhealthy tested positive tested negative 40 10 45 Let E-randomly selected person is infected and let F- randomly selected person tested positive for the disease Find the following (a) P(ENF)= (b) P(EF) (c) P(F|E)= (d) Are E and F independent?

Answer 1

5)

(a)

(b) $P(E^{c})=1-P(E)=1-0.15=0.85$

(c)

(d)

6)

	Infected	healthy $E^{c}$	Total
tested positive	40	5	45
tested negative $F^{c}$	10	45	55
Total	50	50	100

a)

b)

c)

0.8 n(E)50 10

d)

Hence E and F are not independent