With probability 0.001, a prize of $499 is won in the Michigan Daily Lottery when a $1 straight bet is placed. Let Y equal the number of $499 prizes won by a gambler after placing n straight bets. Note that Y is b(n, 0.001). After placing n = 2000 $1 bets, the gambler is behind or even if {Y ≤ 4}. Use the Poisson distribution to approximate P(Y ≤ 4) when n = 2000.

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A prize of $499 is won in the Michigan Daily Lottery with probability 0.001 when a $1 straight bet is placed. Let Y is the number of $499 prizes won by a gambler after placing n straight bets.

Y~B(n, .001). We have to find the probability that P(Y4) after placing n= 2000 $1 bets.