Question

If $3$ winning tickets are drawn from an urn of $100$ tickets, then what is the probability of winning a person who buys $4$ tickets?

Answer 1

$probabilityofsuccess=\left(\frac{3}{100}\right)probabilityofnotsuccess=\left(\frac{97}{100}\right)P\left(winononeticket\right)+P\left(winontwoticket\right)+P\left(winonthreeticket\right)={}^4{C}_1\times \left[\right(\frac{3}{100})\times (\frac{97}{100}{)}^3\left]{+}^4{C}_2\right(\frac{3}{100}{)}^2\left(\frac{97}{100}{)}^3{+}^4{C}_3\right(\frac{3}{100}{)}^3\left(\frac{97}{100}\right){=}^4{C}_1\left(\frac{3\times {97}^3}{{10}^8}\right){+}^4{C}_2\left(\frac{3^2\times {97}^3}{{10}^8}\right){+}^4{C}_3\left(\frac{3^3\times 97}{{10}^8}\right)$