Probability

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Aishwarya1204: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Oct 14, 2012 1:08 am

by Aishwarya1204 » Fri Oct 19, 2012 12:16 pm

If a fair coin is tossed 3 times, what is the probability that it will turn up heads exactly twice?

answer : [spoiler] 3/8[/spoiler]

Is there any way of doing this without having to list out the possibilities like
HHH HHT HTT THT etc.

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Source: Beat The GMAT — Problem Solving | Fri Oct 19, 2012 12:16 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Oct 19, 2012 12:45 pm

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mariofelixpasku: Senior | Next Rank: 100 Posts; Posts: 41; Joined: Sun Sep 23, 2012 4:26 am; Thanked: 2 times

by mariofelixpasku » Fri Oct 19, 2012 1:04 pm

imagine it like this Yes Yes No (YYN)

then we would have 1/2 * 1/2 * 1/2 = 1/8

but we are not done yet cause we have to multiply it with the number of possibilities the 2 Y can be arranged among the 3 spots of YYN.

therefore we have 1/8 * 3P3/2! = 1/8 * 3!/2! = 3/8

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

by Brent@GMATPrepNow » Sat Oct 20, 2012 7:26 am

Aishwarya1204 wrote:If a fair coin is tossed 3 times, what is the probability that it will turn up heads exactly twice?

answer : [spoiler] 3/8[/spoiler]

Is there any way of doing this without having to list out the possibilities like
HHH HHT HTT THT etc.

I think that listing is a great way to solve this question. Too many students discount this approach.

Here's a more mathematical approach:
P(exactly 2 heads) = P(THH OR HTH OR HHT)
= P(THH) + P(HTH) + P(HHT)
= (1/2)(1/2)(1/2) + (1/2)(1/2)(1/2) + (1/2)(1/2)(1/2)
= (1/8) + (1/8) + (1/8)
= [spoiler]3/8[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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