Probability problem

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auppala: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Jan 27, 2013 2:19 am

Probability problem

by auppala » Tue Mar 05, 2013 10:27 am

The probability that a teacher will give an unannounced test during any class meeting is 1/5.If a student is absent twice,then the probability that the student will miss at least one test is
A.4/5
B.2/5
C.7/75
D.9/25
E.8/25

Not sure what the official answer is. Confused between two of the options. Help please !

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Source: Beat The GMAT — Problem Solving | Tue Mar 05, 2013 10:27 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Tue Mar 05, 2013 10:36 am

auppala wrote:The probability that a teacher will give an unannounced test during any class meeting is 1/5.If a student is absent twice,then the probability that the student will miss at least one test is

Probability of missing at least one test = Probability of missing test in only one day + Probability of missing test on both the day

Probability of missing test in only one day = (Probability of happening test on one of the day he was absent)*(Probability of not happening test on the other day he was absent) = (1/5)*(1 - 1/5) = (1/5)*(4/5) = 4/25

Now the above can happen in two ways : {test on first day, no test on second day} or {no test on first day, test on second day}

Hence, probability of missing test in only one day = 2*(4/25) = 8/25

And, probability of missing test on both the day = (1/5)*(1/5) = 1/25

Hence, required probability = 8/25 + 1/25 = 9/25

The correct answer is D.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 05, 2013 10:37 am

auppala wrote:The probability that a teacher will give an unannounced test during any class meeting is 1/5.If a student is absent twice,then the probability that the student will miss at least one test is
A.4/5
B.2/5
C.7/75
D.9/25
E.8/25

Questions with "at least" are often great candidates for using the complement.
That is: P(Event A occurs) = 1 - P(Event A does not occur)

So, P(miss at least 1 test) = 1 - P(miss no tests)

P(miss no tests)
P(miss no tests) = P(no test on day 1 AND no test on day 2)
= P(no test on day 1) X P(no test on day 2)
= (4/5) X (4/5)
= 16/25

So, P(miss at least 1 test) = 1 - P(miss no tests)
= 1 - 16/25
= [spoiler]9/25 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com