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Experimental/Empirical Probability

A has 3 share...

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 for A to loss = $\frac{^{9} C_{3}}{^{12} C_{3}}$
probability for A to win = $1 - \frac{^{9} C_{3}}{^{12} C_{3}} = 1 - \frac{84}{220} = \frac{136}{220}$
probability for B to loss = $\frac{^{6} C_{2}}{^{8} C_{2}}$
probability for A to win = $1 - \frac{^{6} C_{2}}{^{8} C_{2}} = 1 - \frac{15}{28} = \frac{13}{28}$

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