Question

What is the possibility of getting at least 6 heads if eight coins are tossed simultaneously?

• A. $\frac{37}{256}$
• B. $\frac{25}{57}$
• C. $\frac{1}{13}$
• D. $\frac{5}{27}$

Answer 1

The correct option is A $\frac{37}{256}$

We have, $p=\frac{1}{2},q=\frac{1}{2},n=8$Probability (at least 6 heads) $={}^8{C}_6\times {\left(\frac{1}{2}\right)}^6\times {\left(\frac{1}{2}\right)}^2+{}^8{C}_7\times {\left(\frac{1}{2}\right)}^7\left(\frac{1}{2}\right)+{}^8{C}_8{\left(\frac{1}{2}\right)}^8$$=(\frac{8\times 7}{1\times 2}+8+1){\left(\frac{1}{2}\right)}^8$$=37\times \frac{1}{256}=\frac{37}{256}$