Question

A has $3$ shares in a lottery containing $3$ prizes and $9$ blanks, B has $2$ shares in a lottery containing $2$ prizes and $6$ blanks. Compare their chances of success.

Answer 1

Probability of A to lose $=\frac{{}^{9}C_3}{{}^{12}C_3}=\frac{84}{220}$

Probability that A wins $=1-\frac{84}{220}=\frac{136}{220}=\frac{34}{55}$

Probability of B to lose $=\frac{{}^{6}C_2}{{}^{8}C_2}=\frac{15}{28}$

Probability that B wins$=1-\frac{15}{28}=\frac{13}{28}$

Comparing the chances of victory = $\frac{34}{55}:\frac{13}{28}$

As we can see from the comparison that A has more chances to win.