A lot of 10 components contains 3 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let She the event that the second component drawn is defective.

a. Find P(A).

b. Find P(B|A).

c. Find P(A ∩ B).

d. Find P(Ac∩B).

e. Find P(B).

f. Are A and B independent? Explain.

There are 10 components with 3 that are defective:

A = event that the first component is defective

B = event that the second component is defective

b) P(A) = this is the probability that the first component is defective:

= number of defective component/total number of component

P(A) = 3/10 = 0.3

b) P(B|A) = the probability that the second component is defective after the first defective component. Since A has occurred:

= number of defective component left/total number of component left

P(B|A) = 2/9 = 0.22

c) P(A ∩ B) = probability that both are defective i.e. A and B occurring

= 3/10 * 2/9

P(A ∩ B) = 6/90 = 0.06

d) P(Ac ∩ B) = probability that A is not defective and B is defective

P(Ac) = 1 - 3/10 = 7/10 = 0.7

∴ P(Ac ∩ B) =7/10 * 2/9 = 14/90 = 0.16

e) P(B) = probability that the second component is defective

= 2/9 = 0.22

f) B is dependent on A because the defective component is not replaced after the first selection. There would be 9 items left after the first selection of which 2 are defective.

Step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: