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14.Probability
hard
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is
A
$\frac{{255}}{{256}}$
B
$\frac{{127}}{{128}}$
C
$\frac{{63}}{{64}}$
D
$\frac{1}{2}$
(JEE MAIN-2017)
Solution
Required probability $=1-\{\mathrm{P}(\text { All Head })+\mathrm{P}$
(All Tail)
${=1-\left\{\frac{1}{2^{8}}+\frac{1}{2^{8}}\right\}} $
${=1-\left\{\frac{1}{2^{7}}\right\}} $
${=1-\left\{\frac{1}{128}\right\}=\frac{127}{128}}$
Standard 11
Mathematics
