Question

A bin contains a total of 20 batteries, of which 6 are defective. If you select two at random, without replacement, determine the probability that:
a. none of the batteries is good.
b. at least one battery is good.

Answer 1

do you know how to start this

Answer 2

not exactly

Answer 3

lets use combination notation

Answer 4

a) in the 20 batteries, there are 6 defective and 14 functional.

none of them are good. so you know that both are picked from the defective set

Answer 5

( 6 choose 2 ) * (14 choose 0) / ( 20 choose 2 )

Answer 6

14 choose zero since we are not picking any from the set of 14 functional

Answer 7

Ok so (6 C 2) * (14 C 0) / (20 C 2), but we are trying to determine the chance/probability of a. draw a battery the is not functional, and b. at least one battery is functional.

Answer 8

right, thats for a)

Answer 9

for b) you want probability of choosing 1 defective + probability of choosing 2 defective.
it is easier if you use complement

Answer 10

it is easier to do the complement

Answer 11

let X = # of defective when you choose 2
possibilities for X is
X = 0,1,2

Answer 12

a) P(X = 0 )

b) P ( X >= 1)

Answer 13

now for b) we can do

P(X >= 1 )= 1 - P( x < 1)

but P( X < 1) = P( X = 0)

so b) 1 - P( X = 0) , which we got from part a)