Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Jovanmommy_13

What is the probability of flipping a coin 8 times and getting heads 3 times? Round your answer to the nearest tenth of a percent. A.21.9% B.10.9% C.3.1% D.27.3%

  • one year ago
  • one year ago

  • This Question is Closed
  1. ZeHanz
    Best Response
    You've already chosen the best response.
    Medals 0

    If you get head3 3 times, you also get tails 5 times. So there are only two possible outcomes. Each of the two outcomes has possibility 1/2. Say X is the number of heads when flipping 8 times. Then X is binomially distributed. The distribution function for such a process is:\[P(X=3)=\left(\begin{matrix}8 \\ 3\end{matrix}\right)p^3(1-p)^{5}=\left(\begin{matrix}8 \\ 3\end{matrix}\right)\left(\frac{1}{2}\right)^3\left(\frac{1}{2}\right)^5=\left(\begin{matrix}8 \\ 3\end{matrix}\right)\left(\frac{1}{2}\right)^8\]If you find this a little intimidating, you're right ;) It looks more complicated than it actually is. One possible outcome would be: hhttthtt. The chance of getting precisely this outcome is:\[\left( \frac{ 1 }{ 2 }\right)^3 \cdot \left( \frac{ 1 }{ 2 }\right)^5 = \left( \frac{ 1 }{ 2 }\right)^8 \]But this is not the only way go get 3 heads and 5 tails. Any combination of 3xh and 5xt would be ok. That is what the 8 above 3(between brackets) is about. It is a binomial coefficient. It is calculated as follows:\[\left(\begin{matrix}8 \\ 3\end{matrix}\right)=\frac{ 8! }{ 3!5! }=\frac{ 6 \cdot 7 \cdot 8 }{ 2 \cdot 3? }=56\]So there are 56 ways to get 3xh and 5xt. If you now multiply 56 and the outcome of (1/2)^8, you'll have the answer. Multiply that with 100 to get a percentage!

    • one year ago
  2. Jovanmommy_13
    Best Response
    You've already chosen the best response.
    Medals 0

    I can't figure it out

    • one year ago
  3. ZeHanz
    Best Response
    You've already chosen the best response.
    Medals 0

    \[56 \cdot \left( \frac{ 1 }{ 2 } \right)^8=56 \cdot \frac{ 1 }{ 2^8 }=\frac{ 56 }{ 256 }=0.21875\]So times 100 and rounding off gives 21.9%

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.