Question

Suppose there are 4 defective batteries in a drawer with 10 batteries in it. A sample of 3 is taken at random without replacement. Let X denote the number of defective batteries in the sample. Find the probability that the sample contains

a) Exactly one defective battery

b) at most one defective battery.

c) at least one defective battery.

Answer 1

TOPIC:Hypergeometric distribution.
= Define Na Total no. of batteries in the drawer = 10; M = Total no. of defective batteries in the drawer = 4. n = sample size = 3. del, X 2 No. of defective batteries in the sample. (Here, the sampling is done without) replacement. *r Hypergeometrie (N=10, M34, na 3 en The ping of x is - = P (x=x) = { - ; x = max. (o, M+n-N), -, min. (mm) s otherwise . [ sere, max. (o, n+M-N) . L = max. (o, 3+4=10 = max. (0, -3) -0. and min. (n. m) = min. (3, 4) = 3.) in. The king of x is → =) | P (x=x) =S (4) (6) x=0,1,2,3. otherwise,

a) we need = P(x is exactly one). = p (x=1) ( ) ( ) ( by the pony = 1/2 = 10.50 (Anss. by we need, » P ( x is at most one). = P(xs). = P(x20) +P (x-1). (5)(5) 426) (0) + Cild. ( by the end - 0.6667. | Any

y we need = P ( x is at least one), = P(x>D. = 1-P(x < 1). Llavom porementation = 1-P (x=0) al- (*)(3) {o is the only mass-point of - x, which is <2. IN ) 7 alos 1-16 = 10.8333 (Arab.