The probability of bomb hitting a bridge is $\dfrac12$ and $2$ direct hits
are required to destroy it.What is the probability of the destruction
of bridge if only $5$ bombs are drops ?
$a.)\ 62.32\% \\
\color{green}{b.)\ 81.25\%} \\
c.)\ 45.23\% \\
d.)\ 31.32\% $
I did $4 \times \left(\dfrac12\right)^{5}=125\%$ but the answer given
is option $b.)\ $
I look for a short and simple way.
I have studied maths upto $12$th grade.
Best Answer
The bridge is NOT destroyed, if no bomb or only one bomb hits the bridge. The probability for $0$ hits is $\frac{1}{32}$, the probability for $1$ hit is $\frac{5}{32}$. The probability of desctruction is $1-\frac{1}{32}-\frac{5}{32}$