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.

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Solution

## 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.

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