Four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not. The candidates are interviewed at random, and the first qualified candidate interviewed will be hired. The outcomes are the sequences of candidates that are interviewed. So one outcome is 2, and another is 431.

a. List all the possible outcomes.

b. Let A be the event that only one candidate is interviewed. List the outcomes in A.

c. Let B be the event that three candidates are interviewed. List the outcomes in B.

d. Let C be the event that candidate 3 is interviewed. List the outcomes in C.

e. Let D be the event that candidate 2 is not interviewed. List the outcomes in D

f. Let E be the event that candidate 4 is interviewed. Are A and E mutually exclusive? How about B and E, C and E, D and E?

a)

b) A={1, 2}

c) B={341, 342, 431, 432}

d) C={31, 32, 341, 342, 431, 432}

e) D={1, 31, 41, 341, 431}

f) E={41, 42, 341, 342, 431, 432}

Step-by-step explanation:

We know that four candidates are to be interviewed for a job. Two of them, numbered 1 and 2, are qualified, and the other two, numbered 3 and 4, are not.  

a) We get a set of all possible outcomes:

b) Let A be the event that only one candidate is interviewed.

We get a set of all possible outcomes:

A={1, 2}

c) Let B be the event that three candidates are interviewed.

We get a set of all possible outcomes:

B={341, 342, 431, 432}

d)  Let C be the event that candidate 3 is interviewed.

We get a set of all possible outcomes:

C={31, 32, 341, 342, 431, 432}

e) Let D be the event that candidate 2 is not interviewed.

We get a set of all possible outcomes:

D={1, 31, 41, 341, 431}

f) Let E be the event that candidate 4 is interviewed.

We get a set of all possible outcomes:

E={41, 42, 341, 342, 431, 432}

We conclude that the events A and E are mutually exclusive.  

We conclude that the events B and E are not mutually exclusive.

We conclude that the events C and E are not mutually exclusive.

We conclude that the events D and E are not mutually exclusive.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

it’s supposed to be -4+45=41

step-by-step explanation: