Question

Graph a sample space for the experiments:

a. Drawing 3 screws from a lot of right-handed and lefthanded screws.

b. Rolling a die until the first Six appears.

c. Drawing gaskets from a lot of 10, containing one defective D, unitil D is drawn, one at a time and assuming sampling without replacement, that is, gaskets drawn are not returned to the lot.

d. In drawing 2 screws from a lot of right-handed and left-handed screws, let A, B, C, D mean at a least 1 right-handed, at least 1 left-handed, 2 right-handed, 2 left-handed, respectively. Are A and B mutually exclusive? C and D?

Answer 1

(a) SAMPLE SPACE FOR DRAWING 3 SCREWS FROM A LOT OF RIGHT HANDED AND LEFT HANDED SCREWS:

The sample space is represented in the form of where

X- First draw ; Y- Second draw and Z- Third draw

Drawing left-handed screw be denoted as L

Drawing right-handed screw be denoted as R

Now SAMPLE SPACE is given by,

(b) ROLLING A DIE UNTIL FIRST SIX APPEARS:

A die is thrown repeatedly until a six appears. Since the number of times is not mentioned, the sample space will be infinite.

Therefore, the SAMPLE SPACE is given by,

(c) There are totally 10 lots. So sample space is

_. Number of ways to select a defective gasket without replacement from a lot of 10 is 10C_1.

(d) The sample space for drawing 2 screws from a lot of right-handed and left-handed screws is given by,

Let A be the event for drawing atleast 1 right handed screw.

Let B be the event for drawing atleast 1 left handed screw.

Let C be the event for drawing 2 right handed screws.

Let D be the event for drawing 2 left handed screws.

Thus P(A)=3./4 ; P(B)=3/4 ; P(C)=1/4 and P(D)=1/4

Inorder to prove that the events A and B are mutually exclusive, we should show that is a null set or .

Now and

  

Thus is not a null set and .

Hence A and B are not mutually exclusive.

TO PROVE C AND D ARE MUTUALLY EXCLUSIVE:

{Since there are no elements in common} and

Thus the events C and D are mutually exclusive.