Question

A junk box in your room contains eighteen old​ batteries, seven of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome. ​a) The first two you choose are both good. ​b) At least one of the first three works. ​ c) The first four you pick all work. ​d) You have to pick five batteries to find one that works.

Answer 1

0.3595, 0.9571,0.1078,0.00899

Explanation:

Given that a junk box in your room contains eighteen old​ batteries, seven of which are totally dead.

To find out the following probabilities

a) Prob the first two are good =Prob of selecting 2 from 11 good batteries

=
`(11C2)/(18C2) =(110)/(18(17)) \\=0.3595`

b) Atleast one of the first three works

=P(1 or 2 or 3) = 1-P(0)

=
`1-(7C3)/(18C3) \\=0.9571`

c) The first four work = Prob of picking all 4 from 11 good ones

=
`(11C4)/(18C4) \\=0.1078`

d) You have to pick five batteries to find one that works.

= Prob first 4 are defective and 5th is good

=
`(7C4)/(18C4) *(11C1)/(14C1)` =0.00899

(This is because once 4 defective removed we have remaining 3 defective and 11 good in total 14)