anonymous
  • anonymous
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%
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ZeHanz
  • ZeHanz
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!
anonymous
  • anonymous
I can't figure it out
ZeHanz
  • ZeHanz
\[56 \cdot \left( \frac{ 1 }{ 2 } \right)^8=56 \cdot \frac{ 1 }{ 2^8 }=\frac{ 56 }{ 256 }=0.21875\]So times 100 and rounding off gives 21.9%

Looking for something else?

Not the answer you are looking for? Search for more explanations.