A test for the presence of a certain disease has probability

.20 of giving a false-positive reading (indicating that an individual has the disease when this is not the case) and 1 2 P(X , 20)

P(20 # X) P(20 # X) 5 1 2 p 2 q 5 P(draw)

p 5 P(S) q 5 P(F)

p(x) 5 P(X 5 x)

x 5 10, 11,

c, 19 X 5 the number P(F) 5 1 2 p P(S) 5 p S 5 5A wins a game6 m 5 4 X 5 the number a 5 2 a 5 2 X 5 the number probability .10 of giving a false-negative result. Suppose that ten individuals are tested, five of whom have the disease and five of whom do not. Let of positive readings that result.

a. Does X have a binomial distribution? Explain your reasoning.

b. What is the probability that exactly three of the ten test results are positive?