Question

In the state lottery, your chances of winning $2-$5 are 1 in 3. All winners are eligible for the Big Bucks drawing where the chances of winning are 1 in 10. All winners in the Big Bucks drawing get a chance for the one Mega Bucks prize where the odds are 1 in 50. What are your chances of winning the Mega Bucks prize if you buy one lottery ticket?

A. 1 in 30
B.1 in 150
C.1 in 500
D.1 in 1,500​

Answer 1

The answer is D.

Explanation:

To calculate the chances of winning the Mega Bucks prize, we need to first calculate the probability of winning at each stage of the lottery.

The probability of winning $2-$5 in the state lottery is 1 in 3, or 1/3. This means that the probability of not winning $2-$5 is 2 in 3, or 2/3.

The probability of winning the Big Bucks drawing is 1 in 10, or 1/10. This means that the probability of not winning the Big Bucks drawing is 9 in 10, or 9/10.

The probability of winning the Mega Bucks prize is 1 in 50, or 1/50. This means that the probability of not winning the Mega Bucks prize is 49 in 50, or 49/50.

To find the probability of winning the Mega Bucks prize if you buy one lottery ticket, we need to multiply the probabilities of winning at each stage:

P(Mega Bucks) = P(state lottery) x P(Big Bucks) x P(Mega Bucks)

P(Mega Bucks) = (1/3) x (1/10) x (1/50)

P(Mega Bucks) = 1/1,500

Therefore, the chances of winning the Mega Bucks prize if you buy one lottery ticket are 1 in 1,500. The answer is D.