Question

can someone show me how to do this thank you please i inned inneeeed it

In a group of 20 batteries, 3 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. Number good 0 2 P(Number good) (Round to three decimal places as needed.)

Answer 1

a)

Let X = Number of batteries are good.

For X = 0 , That is both batteries are defective.

Number of ways to get 2 defective batteries from 3 defective = ³C₂

Total number of ways to get 2 batteries from 20 =  ²⁰C₂

P( X = 0) =  ³C₂ / ²⁰C₂

= 3 / 190

= 0.016

For X = 1

That is we choose 1 out of 2 batteries is good.

P(1 good battery) = P( one good) * P(one defective)

= ¹⁷C₁ * ³C₁ / ²⁰C₂

= 0.268

For X = 2

That is we choose both good batteries from 17 good batteries.

P( Both good) = ¹⁷C₂ / ²⁰C₂

= 136 / 190

= 0.716

Number of good	0	1	2
Probability of good	0.016	0.268	0.716

b)

Let X be number of good batteries

P(X) be probability of good batteries

E(X) = $\sum$ X * P(X)

= 0 * 0.016 + 1* 0.268 + 2 * 0.716

= 1.7

Expected number of good batteries = 1.7

c)

Standard deviation = Sqrt [ $\sum$ X² * P(X) - [E(X) ]² ]

= Sqrt[ (0² * 0.016 + 1² * 0.268 + 2² * 0.716 ) - 1.7² ]

= 0.4919