Probability

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vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

Probability

by vaibhav101 » Sat Jun 16, 2018 12:56 am

the probability that a teacher will give a surprise test during any class meeting is 1/5. If a student is absent on 2 days, then the probability that he will miss at least 1 test is.

A 24/25
B 1/25
C 16/25
D 9/25
E 7/25

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Source: Beat The GMAT — Problem Solving | Sat Jun 16, 2018 12:56 am

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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 » Sat Jun 16, 2018 4:37 am

vaibhav101 wrote:the probability that a teacher will give a surprise test during any class meeting is 1/5. If a student is absent on 2 days, then the probability that he will miss at least 1 test is.

A 24/25
B 1/25
C 16/25
D 9/25
E 7/25

First, if P(test) = 1/5, then p(NO test) = 1 - 1/5 = 4/5

NOTE: 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
= 9/25
Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jun 20, 2018 4:09 pm

vaibhav101 wrote:the probability that a teacher will give a surprise test during any class meeting is 1/5. If a student is absent on 2 days, then the probability that he will miss at least 1 test is.

A 24/25
B 1/25
C 16/25
D 9/25
E 7/25

We can use the equation:

P(miss at least one test) = 1 - P(will miss zero tests)

P(miss zero tests) = 4/5 x 4/5 = 16/25

P(miss at least one test) = 1 - 16/25 = 9/25

Answer: D

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