Question

One woman won $1 million from the lottery. Years later she won $1million again. In the first game she beat the odds of 1 in 5.2 million to win. In the second she beat odds of 1 in 805,600.

Answer 1

Given that:

Amount win from the scratch-off game = $1 million

The individual beat odds of 1 in 6.2 million to win in the first game and in the second game, the individual beat odds of 1 in 805600.

Let A and B denote the events "Won in first game" and "Won in the second game".

Then, find P(A) and P(B)5

$\begin{gathered} P(A)=\frac{1}{5.2\text{ Million}} \\ =\frac{1}{5.2\times10^6} \\ =1.92\times10^{-7} \end{gathered}$$\begin{gathered} P(B)=\frac{1}{805600} \\ =1.24\times10^{-6} \end{gathered}$

(a) P(Indiviual win in both games)

$\begin{gathered} =P(A)\times P(B) \\ =1.92\times10^{-7}\times1.24\times10^{-6} \\ =2.381\times10^{-13} \end{gathered}$

(b) P(Individual win twice in the second game)

$\begin{gathered} =P(B)\times P(B) \\ =1.24\times10^{-6}\times1.24\times10^{-6} \\ =1.54\times10^{-12} \end{gathered}$