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Suppose that in a day, a casino receives 2500 bets on a certain color(red or black) on one particular roulette wheel. Each bet is only a dollar bet. The house(casino) has 20 in 38 chances to win. Estimate the chance that the house will win at least 100 dollars. Write your answer as a decimal

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closed as off-topic by Em., user1551, user91500, Especially Lime, Claude Leibovici Apr 17 '17 at 7:51

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  • $\begingroup$ Hi and welcome to the site. Please show any own attempts you've made. $\endgroup$ – mathreadler Apr 17 '17 at 6:47
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Let $X$ be the number of dollars won by the house.

We know that $X \sim B\left(2500,\dfrac{10}{19}\right)$.

We can estimate it by $N(1316,623)$.

So, the required probability (using continuity correction):

$\begin{array}{cl} =&P(X \ge 99.5) \\ =&P\left(Z \ge \dfrac{99.5-1316}{623} \right) \\ =&P\left(Z \ge -1.9526 \right) \\ =&P\left(Z \le 1.9526 \right) \\ =&0.9744 \end{array}$

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