Question

Eight coins are tossed at a time, the probability of getting atleast 6 heads up, is

• A. $\frac{7}{64}$
• B. $\frac{57}{64}$
• C. $\frac{37}{256}$
• D. $\frac{229}{256}$

Answer 1

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

Total coins = 8
Probability of getting head = $\frac{1}{2}$
And probability of getting tail =$\frac{1}{2}$
Hence, probability of getting at least 6 heads up
${=}^8{C}_6{\left(\frac{1}{2}\right)}^6{\left(\frac{1}{2}\right)}^2{+}^8{C}_7{\left(\frac{1}{2}\right)}^7{\left(\frac{1}{2}\right)}^1{+}^8{C}_8{\left(\frac{1}{2}\right)}^8{\left(\frac{1}{2}\right)}^0=\frac{{}^8{C}_6{+}^8{C}_7{+}^8{C}_8}{2^8}=\frac{{}^8{C}_2{+}^8{C}_1+1}{2^8}=\frac{37}{256}$