Suppose you play 1000 spins of roulette and on each time you

Suppose you play 1000 spins of roulette and on each time you bet that the ball will land on a red number. Use the normal approximation to compute the probability that you win more than 500 times.

Other Information: On a standard roulette wheel, there are 36 numbers 1-36, half oif which are red and half of which are black. There are also the numbers zero \"0\", and double zero \"00\", which are colored green.

Solution

probability of your number hitting exactly x times is combin(1000,x)*(1/38)^x*(37/38)^1000-x. The following table shows the probability of all number of hits from 0 to 6 and the total.

Wins in 1000 Roulette Bets

So the answer is 0.00000177564555, or 1 in 563175. I hope this didn