Determine the probability of winning a grand prize

A lottery promises to award 10 grand prize trips to Hawaii and sells 5 400 000 tickets.

a)Determine the probability of winning a grand prize if you buy 1 ticket.

The answer is 1/ 540 000 , so it seems like all they did is move one decimal over to the left, but I don't understand why, could you explain if there is a better way to get the answer.

b) How many tickets do you need to buy in order to have a 5% chance of winning a grand prize?

How do you find this? like 1/x= 5%? or sorry, I have no idea.

Thanks so much.

A lottery promises to award 10 grand prize trips to Hawaii and sells 5 400 000 tickets.

a)Determine the probability of winning a grand prize if you buy 1 ticket.

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There are 10 prizes in 5,400,000. So the probability of winning from one ticket is \(\displaystyle \L\\\frac{10}{5,400,000}=\frac{1}{540,000}\)

b) How many tickets do you need to buy in order to have a 5% chance of winning a grand prize?

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It would something like \(\displaystyle \frac{x}{540,000}=0.05\). Solve for x.

for part b) how come its x/ 540 000, and not over 5 400 000?

Because there's 10 grand prozes in the 5,400,000 tickets.