A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
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%
 2 years ago
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%

This Question is Closed

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0If 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:\[P(X=3)=\left(\begin{matrix}8 \\ 3\end{matrix}\right)p^3(1p)^{5}=\left(\begin{matrix}8 \\ 3\end{matrix}\right)\left(\frac{1}{2}\right)^3\left(\frac{1}{2}\right)^5=\left(\begin{matrix}8 \\ 3\end{matrix}\right)\left(\frac{1}{2}\right)^8\]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!

Jovanmommy_13
 2 years ago
Best ResponseYou've already chosen the best response.0I can't figure it out

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.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%
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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
 Engagement 19 Mad Hatter
 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.