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8 coins are tossed simultaneously. The probability of getting at least 6 heads is
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Verified Answer
The correct answer is:
$\frac{37}{256}$
In tossing of coin getting $r$ head out of $n$ tossing
$={ }^{n} C_{r} \cdot\left(\frac{1}{2}\right)^{n}$
$\therefore \quad$ Required probability
$=\left({ }^{8} \mathrm{C}_{6}+{ }^{8} \mathrm{C}_{7}+{ }^{8} \mathrm{C}_{8}\right)\left(\frac{1}{2}\right)^{8}$
$=(28+8+1) \times \frac{1}{256}=\frac{37}{256}$
$={ }^{n} C_{r} \cdot\left(\frac{1}{2}\right)^{n}$
$\therefore \quad$ Required probability
$=\left({ }^{8} \mathrm{C}_{6}+{ }^{8} \mathrm{C}_{7}+{ }^{8} \mathrm{C}_{8}\right)\left(\frac{1}{2}\right)^{8}$
$=(28+8+1) \times \frac{1}{256}=\frac{37}{256}$
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