Question

In a group of 20 ​batteries, 5 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?   

Answer 1

Number of dead batteries are 5 among 50 batteries

Hence good batteries would be 15

Probability of good batteries P = 15 / 20 = 0.75

2 battereis are selected at random

Part a)

X ~ B ( n = 2 , P = 0.75 )

X	P ( X )
0	0.0625
1	0.3750
2	0.5625

Part b)

Mean = n * P = ( 2 * 0.75 ) = 1.5

Part c)

Variance = n * P * Q = ( 2 * 0.75 * 0.25 ) = 0.375
Standard deviation = √(variance) = (0.375) = 0.6124