Question

In a group of

10

​batteries,

4

are dead. You choose 2 batteries at random.

​a) Create a probability model for the number of good batteries you get.

​b) What's the expected number of good ones you​ get?

​c) What's the standard​ deviation?

​a) Create a probability model.

Answer 1

Answer:

a)

Given,

Number of batteries = 10

Defective = 4

2 batteries selected randomly

X	0	1	2
P(x)	6C0*4C2 / 10C2 = 0.133	6C1*4C1 / 10C2 = 0.533	6C2*4C0 / 10C2 = 0.333

b)

To give expected value = x*P(x)

= 0*0.133 + 1*0.533 + 2*0.333

= 0 + 0.533 + 0.666

E(X) = 1.199

c)

E(X^2) = x^2*P(x)

= 0^2*0.133 + 1^2*0.533 + 2^2*0.333

= 0 + 0.533 + 1.332

= 1.865

Standard deviation = sqrt(E(X^2) - (E(X))^2)

= sqrt(1.865 - 1.199^2)

= sqrt(1.865 - 1.438)

= sqrt(0.427)

= 0.6535