Problem

Once a woman won $\$ 1$ million in a scratch-off game from a lottery. Some years later, she won $\$ 1$ million in another scratch-off game. In the first game, she beat odds of 1 in 4.2 million to win. In the second, she beat odds of 1 in 805,600 . (b) The probability that an individual would win $\$ 1$ million twice in the second scratch-off game is (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest tenth as needed.)

Solution

Step 1 :A woman won $1 million twice in a scratch-off game. The odds of winning the second scratch-off game are 1 in 805,600.

Step 2 :The probability of winning the second scratch-off game is calculated by taking the reciprocal of the odds, which gives us approximately \(1.2413108242303872 \times 10^{-6}\).

Step 3 :To find the probability of winning twice, we square the probability of winning once, because the two events are independent. This gives us approximately \(1.5408525623515232 \times 10^{-12}\).

Step 4 :Final Answer: The probability that an individual would win $1 million twice in the second scratch-off game is approximately \(\boxed{1.5 \times 10^{-12}}\).

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Source: https://solvelyapp.com/problems/18370/

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