Question

A batch of 587 containers for frozen orange juice defective. Two are se (a) What is the probability that the second one selected is defective given that the first one was contains 5 that are defective. Two are selected, at random, without replacement from the batch. Round your answers to four decimal places (e.g. 98 (c) What is the probability that both are acceptable?

Answer 1

There are 5 defective containers, so non defectivecontainers is 582

Number of ways of choosing 2 from 587, is $\binom{587}{2}=171991$

Hence probability if first one is defective is

${\binom{5}{1}\binom{582}{1} \over 171991}+ {\binom{5}{2}\over 171991}={2920\over 171991}$

Hence the required probability is

${{\binom{5}{2}/ 171991}\over {2920/171991}}={10\over 2920}=0.0034$

b) Required probability is

${\binom{5}{2}\over 171991}={10\over 171991}\approx 0.0001$

c) Required probability is

${\binom{582}{2}\over 171991}={169071\over 171991}\approx 0.9830$