Question

A box has 10 tickets in it, two of which are winning tickets. You draw a ticket at random. If it's a winning ticket, you win. If not, you get another chance, as follows: your losing ticket is replaced in the box by a winning ticket (so now there are 10 tickets, as before, but 3 of them are winning tickets). You get to draw again, at random. Which of the following are legitimate methods for using simulation to estimate the probability of winning? I. Choose, at random, a two-digit number. If the first digit is 0 or 1, you win on the first draw; If the first digit is 2 through 9, but the second digit is 0, 1, or 2, you win on the second draw. Any other two-digit number means you lose. Il. Choose, at random, a one-digit number. If it is 0 or 1, you win. If it is 2 through 9, pick a second number. If the second number is 8, 9, or 0, you win. Otherwise, you lose. Ill. Choose, at random, a one-digit number. If it is 0 or 1, you win on the first draw. If it is 2, 3, or 4, you win on the second draw; If it is 5 through 9, you lose.

Answer 1

To estimate the probability of winning in this scenario, we can simulate the drawing of tickets multiple times and record the number of times a winning ticket is drawn. Method I is not a legitimate method for estimating the probability of winning, but Methods II and III are legitimate methods.

Step-by-step explanation:

To estimate the probability of winning in this scenario, we can simulate the drawing of tickets multiple times and record the number of times a winning ticket is drawn. The more simulations we run, the more accurate our estimate will be.

Method I of choosing a two-digit number is not a legitimate method for estimating the probability of winning because it does not accurately simulate the random drawing of tickets.

Method II of choosing a one-digit number and then a second number is a legitimate method for estimating the probability of winning. By recording the number of times the conditions for winning are met, we can estimate the probability of winning.

Method III of choosing a one-digit number is also a legitimate method for estimating the probability of winning. By recording the number of times the conditions for winning are met, we can estimate the probability of winning.