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.
Accepted Solution
A:
Answer:0.3595, 0.9571,0.1078,0.00899Step-by-step explanation:Given that a junk box in your room contains eighteen old batteries, seven of which are totally dead. To find out the following probabilitiesa) Prob the first two are good =Prob of selecting 2 from 11 good batteries = [tex]\frac{11C2}{18C2} =\frac{110}{18(17)} \\=0.3595[/tex]b) Atleast one of the first three works=P(1 or 2 or 3) = 1-P(0)= [tex]1-\frac{7C3}{18C3} \\=0.9571[/tex]c) The first four work = Prob of picking all 4 from 11 good ones=[tex]\frac{11C4}{18C4} \\=0.1078[/tex]d) You have to pick five batteries to find one that works.= Prob first 4 are defective and 5th is good= [tex]\frac{7C4}{18C4} *\frac{11C1}{14C1}[/tex] =0.00899(This is because once 4 defective removed we have remaining 3 defective and 11 good in total 14)