Question

4 unbiased coins are tossed $256$ times. The expected frequency of $x$ heads

• A. ${16}^4{C}_x$
• B. ${12}^4{C}_x$
• C. ${12}^4{C}_0$
• D. $8^4{C}_0$

Answer 1

Answer: (A)

${16}^4{C}_x$

In an unbiased coin, the probability of head=probability of tails =$\frac{1}{2}$
Hence for 4 trials, probability of x heads is
$P\left(X\right)$
$={}^4{C}_x\left(\frac{1}{2}{)}^x\right(\frac{1}{2}{)}^{4-x}$
$=\frac{1}{16}\left[{}^4{C}_x\right]$
Hence the expected frequency will be
$256\times \left(\frac{1}{16}\right[{}^4{C}_x\left]\right)$

$=16{}^4{C}_x$