Question

Six unbiased coins are tossed once. The probability of obtaining atleast two heads is :

• A. $63/64$
• B. $57/64$
• C. $1/64$
• D. $1/32$

Answer 1

Answer: (B)

$57/64$

Six unbiased coins are tossed once.
Probability of head in a coin = $\frac{1}{2}$
The probability of obtaining at least two heads is given by $1-$[ The probability of obtaining no heads + The probability of obtaining one heads ]
The probability of obtaining at least two heads
$=1-{[}^6{C}_0{\left(\frac{1}{2}\right)}^0{(1-\frac{1}{2})}^{6-0}{+}^6{C}_1{\left(\frac{1}{2}\right)}^1{(1-\frac{1}{2})}^{6-1}$ ]
$=1-[\frac{1}{64}+\frac{3}{32}$ ]
$=1-[\frac{7}{64}$ ]
$=\frac{57}{64}$