Question

If two coins are tossed $5$ times, then the probability of getting $5$ heads and $5$ tails is

• A. $\frac{63}{256}$
• B. $\frac{1}{1024}$
• C. $\frac{2}{205}$
• D. $\frac{9}{64}$

Answer 1

The correct option is A

$\frac{63}{256}$

Explanation for the correct option:

Finding the probability:

Total number of outcomes when $2$ coins are tossed $5$ times $=2^{10}$.

The cases when there will be $5$ heads and $5$ tails $=\mathrm{H},\mathrm{H},\mathrm{H},\mathrm{H},\mathrm{H},\mathrm{T},\mathrm{T},\mathrm{T},\mathrm{T},\mathrm{T}$

Number of favorable outcomes $=\frac{10\mathrm{ǃ}}{5\mathrm{ǃ}\times 5\mathrm{ǃ}}$

$=252\mathrm{ways}$

$\begin{array}{rcl}\mathrm{Probability}\mathrm{of}\mathrm{getting}5\mathrm{heads}\mathrm{and}5\mathrm{tails}& =& \frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}\\ & =& \frac{252}{2^{10}}\\ & =& \frac{252}{1024}\\ & =& \frac{63}{256}\end{array}$

Hence, the correct option is A.