Need explanation for probability problem.

This topic has 1 expert reply and 6 member replies
akpareek Senior | Next Rank: 100 Posts Default Avatar
Joined
14 Feb 2010
Posted:
38 messages

Need explanation for probability problem.

Post Wed Sep 04, 2013 9:03 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2-flips ?

    A. 3/5
    B. 1/2
    C. 1/5
    D. 1/8
    E. 1/32

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Sep 04, 2013 9:13 am
    akpareek wrote:
    If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 3 flips and not on the last 2-flips?

    A. 3/5
    B. 1/2
    C. 1/5
    D. 1/8
    E. 1/32
    We want P(heads on 1st AND heads on 2nd AND heads on 3rd AND tails on 4th AND tails on 5th)
    = P(heads on 1st) x P(heads on 2nd) x P(heads on 3rd) x P(tails on 4th) x P(tails on 5th)
    = 1/2 x 1/2 x 1/2 x 1/2 x 1/2
    = 1/32 = E

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    Thanked by: akpareek
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Wed Sep 04, 2013 11:20 pm
    Hi akpareek,

    Brent's explanation is spot-on, so I won't rehash it here. What I will point out is that for this type of complex situation (5 tosses), the question is way too simple. So, what is the source of this prompt?

    A far more likely GMAT-style question would be "What is the probability that exactly 3 of the flips are heads?"

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    vinay1983 Legendary Member
    Joined
    14 Aug 2013
    Posted:
    643 messages
    Followed by:
    6 members
    Thanked:
    48 times
    Target GMAT Score:
    650+
    Post Thu Sep 05, 2013 2:23 am
    Rich.C@EMPOWERgmat.com wrote:
    Hi akpareek,

    Brent's explanation is spot-on, so I won't rehash it here. What I will point out is that for this type of complex situation (5 tosses), the question is way too simple. So, what is the source of this prompt?

    A far more likely GMAT-style question would be "What is the probability that exactly 3 of the flips are heads?"

    GMAT assassins aren't born, they're made,
    Rich
    Rich, then what can be the answer for your question?(Explain)

    _________________
    You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

    Post Thu Sep 05, 2013 12:42 pm
    Hi vinay1983,

    With 5 coin flips, here's how you figure out the probability of flipping exactly 3 heads.

    First, we calculate the total number of possible outcomes. Since each coin has 2 outcomes, the total outcomes is 5^2 = 32 total possibilities.

    Now, since it doesn't matter which 3 tosses are heads, we use the combination formula to calculate all the different ways to get 3 heads...

    5c3 = 5!/(3!2!) = 10 ways to get 3 heads.

    Final answer for this question = 10/32 = 5/16

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    vishnum Junior | Next Rank: 30 Posts Default Avatar
    Joined
    31 Aug 2013
    Posted:
    11 messages
    Post Thu Sep 05, 2013 9:35 pm
    Hi Rich,

    In the 10 ways of heads occurring 3 times we will have HTTHH etc.. But in the question we are interested only with HHHTT possibility only. Isn't it?

    Br,
    Vishnu.

    sanjoy18 Senior | Next Rank: 100 Posts Default Avatar
    Joined
    11 Jun 2013
    Posted:
    81 messages
    Followed by:
    1 members
    Thanked:
    7 times
    Post Thu Sep 05, 2013 9:50 pm
    Hi Vishnu,

    "What is the probability that exactly 3 of the flips are heads?"
    Above is the question that Rich posted..then question asked exactly 3 heads rather first three consecutive heads. hence the answer is 5/16

    this problem can be solved by another method.actually it follows binomial probability
    p(x)=probability of getting exactly x head in n trials
    = ncx p^x (1-p)^(n-x)
    here n=5 x=3
    = 5c3 (1/2)^3 (1/2)^2
    = 10*(1/8)*(1/4)
    = 5/16

    Post Thu Sep 05, 2013 11:35 pm
    Hi vishnum,

    It's true of ALL GMAT questions, but in this case, you really need to pay attention to what the question is asking you to solve. My example asked for ANY 3 of the 5 tosses to be heads, not necessarily the first 3. The way that the question is worded will define HOW you have to do the math. In many cases, some of the wrong answers are answers to different questions, so taking the time to understand the question and organize your work is a MUST.

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Best Conversation Starters

    1 AbeNeedsAnswers 125 topics
    2 jjjinapinch 82 topics
    3 richachampion 12 topics
    4 saswata4s 10 topics
    5 NandishSS 10 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Matt@VeritasPrep

    Veritas Prep

    120 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    116 posts
    3 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    93 posts
    4 image description DavidG@VeritasPrep

    Veritas Prep

    75 posts
    5 image description GMATGuruNY

    The Princeton Review Teacher

    62 posts
    See More Top Beat The GMAT Experts