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What’s NewLet’sexplore!Activity 2: Exploring Condition FurtherConsider the situation and answer the questions that follow.A proficiency examination for certain literacy skills was given 100 students.The breakdown of the examination results of the students are shown in the tablebelow.Male (M)Female (F)TotalPass (P)243660Fail (F)1624404060100Suppose that a student is selected at random from among 100 students whotook the examination.1. Are the eventsPandMindependent? Explain.2. Are the eventsPandFindependent? Explain.3. Find the probability that the students passed the exam, given that he was amale.4. Find the probability that the student was a male given that a passing gradewas received.5. Find the probability that the student was a female, given that a passing gradewas received.
31What Is ItDiscussionA proficiency examination for certain literacy skills was given 100 students.The breakdown of the examination results of the students are shown in the tablebelow.Male (M)Female (F)TotalPass (P)243660Fail (F)1624404060100Suppose that a student is selected at random from among 100 students whotook the examination.Guide QuestionFigure/ Expression/SolutionDiscussion1. Are the eventsPandMindependent?Explain.-We can say that theevents areindependent if?(?|𝑀) = ?(?) ???(𝑀|?) = ?(𝑀)?? ?(? ??? 𝑀)= ?(?)?(𝑀).Let us find the probability of Pgiven that M has occurred andsee if it is different from theprobability of P. So we have,?(?|𝑀) =2440??35and?(?) =60100??35Since theseprobabilities are thesame, events? ??? 𝑀are independent.Pinside the parenthesisrepresents the event“Pass.”You can go backto the given table forreference.2. Are the eventsPandFindependent?Explain?(?|?) =3660??35and?(?) =60100??35Since they are the same,then events P and F arealso independent.3. Find theprobability thatthe studentspassed theexam, given thathe was a male.?(?|𝑀) =2440?? 0.60There are 40 males. Ofthese 40 males, 24passed the proficiencyexamination. So, theprobability is 0.60.Did you get the answer correctly in activity 1? If no, then practice more aboutour previous topic. If yes, then let us continue with our topic today. For us tounderstand more about conditional probability let us look at your answer andmy answer in activity 2.
Guide QuestionFigure/Expression/SolutionDiscussion4.Find theprobability that thestudent was a malegiven that a passinggrade was received.2460?? 0.40
Examples:1. A single fair die is rolled. Let A={3} and B={1,3,5}. Are A and B independent?
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Term
Winter
Professor
NoProfessor
Tags
Conditional Probability, Probability theory

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