Question

If on an average $1$ vessel in every $10$ is wrecked, find the chance that out of $5$ vessels expected $4$ at least will arrive safely.

Answer 1

Probability of a vessel to arrive safely $=\frac{9}{10}$

$\therefore$ Probability of at 5 vessels to arrive safely = Probability of all 5 arriving safely + Probability of 4 arriving safely

$\therefore$ Required probability $={\left(\frac{9}{10}\right)}^5+5\times {\left(\frac{9}{10}\right)}^4\times \left(\frac{1}{10}\right)=\frac{45927}{50000}$