Question

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If two people are selected at random for a task, what is the probability that they will be an engineer and an executive?

A =4/80*2/79+2/80*4/79 or =COMBIN(4,1)*COMBIN(2,1)*COMBIN(74,0)/COMBIN(80,2)

B =4/80*2/79

C =4/80*2/80

D = COMBIN(4,2)*COMBIN(2,2)*COMBIN(74,0)/COMBIN(80,2)

How many ways could people rank the top three cows from a herd of ten.

A 120

B 720

C 210

D 5,040

On a snack tray there are 3 different types of crackers ( a dozen of each) and six different types of cheese ( a half dozen cubes of each). How many different combinations can be made.

A 72

B 18

C 12

D 24

What is the standard deviation of the following probability distribution?

X	0	2	4	6
P(X)	0.20	0.05	0.5	0.25

A 2.06

B 17.2

C 3.6

D 4.24

In a bag of 20 marbles, 25% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets all of the red marbles? Marbles are not replaced.

.008

0.001032

.3

.25

Answer 1

1) option A is correct

A =4/80*2/79+2/80*4/79 or =COMBIN(4,1)*COMBIN(2,1)*COMBIN(74,0)/COMBIN(80,2)

2)
number of ways to choose 3 and rank them from 10 =10*9*8=720

3_)

number of different combinations =3*6 =18

4)

x	P(X=x)	xP(x)	x2P(x)
0	0.200	0.00000	0.00000
2	0.050	0.10000	0.20000
4	0.500	2.00000	8.00000
6	0.250	1.50000	9.00000
total		3.6000	17.2000
	E(x) =μ=	ΣxP(x) =	3.6000
	E(x2) =	Σx2P(x) =	17.2000
	Var(x)=σ2 =	E(x2)-(E(x))2=	4.2400
	std deviation=	σ= √σ2 =	2.06

5)

P(all red marbles)=(5*4*3*2)/(20*19*18*17)=0.001032