Lottery Probability Help (specifically part D)

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April 28th 2010, 04:53 PM
superpowerspacemonkey

Lottery Probability Help (specifically part D)

Consider a 46/9 Lottery...

a)How many tickets are possible?
b)Find the probability of winning first prize

c) Find the probability of NOT winning first prize

d) Find the probability of winning 2nd prize. (To win 2nd prize, you must correctly match 8 of the 9 winning numbers)
April 28th 2010, 10:11 PM
veljko

a) $|\Omega|=$ ${46}\choose {9}$ $= 1.101.716.330$ possible diferents tickets.

b) $p_1 = \frac {1}{1.101.716.330}$

c) $p_2$ (not winning 1. prize) $= 1 - \frac {1}{1.101.716.330} (\approx 1$ :). So, do not play a lottery)

d) $p_3$ (2nd prize) = $\frac{{9 \choose 8}{37 \choose 1}}{{46 \choose 9}} = \frac{9 \cdot 37}{1.101.716.330} = \frac{333}{1.101.716.330} = 333\cdot p_1$ .

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