Results 1 to 7 of 7

Math Help - Coin toss problem

  1. #1
    Member
    Joined
    Jul 2006
    Posts
    90

    Coin toss problem

    1). In 3 fair coin tosses, what is the probability of obtaining exactly 2 tails? (Note In a fair coin toss the 2 outcomes, heads and tails, are equally likely).

    I don't understand why the answer is 3/8??

    2). In a shipment of 1000 light bulbs, 1/40 of the bulbs were defective. What is the ratio of defective bulbs to non-defective bulbs?

    Why is the answer 1/39??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by sarahh View Post
    1). In 3 fair coin tosses, what is the probability of obtaining exactly 2 tails? (Note In a fair coin toss the 2 outcomes, heads and tails, are equally likely).

    I don't understand why the answer is 3/8??
    Exactly two tails means two tails AND one head. There are three different ways that possibility can occur. 3*\left(\frac{1}{2}\right)^3 = \frac{3}{8}

    Quote Originally Posted by sarahh View Post
    2). In a shipment of 1000 light bulbs, 1/40 of the bulbs were defective. What is the ratio of defective bulbs to non-defective bulbs?

    Why is the answer 1/39??
    The amount of light bulbs is useless information... \frac{\frac{1}{40}}{\frac{39}{40}}=\frac{1}{39}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jul 2006
    Posts
    90
    Thanks so much colby--lol number 2 can't believe I didn't see that. Still a little stuck on the first...not sure why it's 3 times a half cubed??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by sarahh View Post
    Thanks so much colby--lol number 2 can't believe I didn't see that. Still a little stuck on the first...not sure why it's 3 times a half cubed??
    Three possibilities; there are three coin tosses that can go like this:

    TTH
    HTT
    THT

    Each one of those has a \frac{1}{8} chance of happening.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jul 2006
    Posts
    90
    Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

    HHH
    TTT
    THH
    HTH
    HHT
    Follow Math Help Forum on Facebook and Google+

  6. #6
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by sarahh View Post
    Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

    HHH
    TTT
    THH
    HTH
    HHT
    Yes, as always in probability, that is one more way of looking at it!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by sarahh View Post
    Ahh ok--so the reason why it's over 8 is because of the other 5 possibilities?? That is:

    HHH
    TTT
    THH
    HTH
    HHT
    When each outcome is equally likely (which they are here), the probabilty is given by


    \displaystyle \frac{\text{Number of successful outcomes}}{\text{Number of possible outcomes}}.


    In your problem, the number of successful outcomes = 3 and the number of possible outcomes = 8. So the probability is 3/8.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Coin toss
    Posted in the Statistics Forum
    Replies: 15
    Last Post: June 5th 2010, 12:59 AM
  2. coin toss
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: May 19th 2010, 04:35 PM
  3. Coin Toss
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: March 7th 2010, 12:00 AM
  4. Explaining the 'coin-toss' problem...
    Posted in the Statistics Forum
    Replies: 4
    Last Post: November 21st 2009, 09:03 AM
  5. coin toss
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 7th 2009, 03:03 AM

Search Tags


/mathhelpforum @mathhelpforum