In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusive. Find the probability that a ticket holder has the indicated winning ticket.
The first three digits in exact order.
To find the probability that a ticket holder has the indicated winning ticket, we need to determine the number of favorable outcomes (winning tickets) and the total number of possible outcomes.
In this case, the ticket holder needs to have the first three digits in exact order. Since there are 10 possible numbers (0-9) for each digit, the number of favorable outcomes is 1 (since there is only one specific winning combination for the first three digits).
The total number of possible outcomes can be calculated by finding the number of possible numbers (10) for each of the first three digits. Since the numbers are drawn with replacement, each digit has 10 possibilities. Therefore, the total number of possible outcomes is 10 × 10 × 10 = 1000.
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 1000
Therefore, the probability that a ticket holder has the indicated winning ticket is 1/1000.
To find the probability of winning with the first three digits in exact order, we need to determine the total number of possible outcomes and the number of favorable outcomes.
In the Numbers Game, there are a total of 10 possible numbers (0-9) that could be drawn for each of the three digits. Since the numbers are drawn with replacement, each digit can be any number from 0 to 9.
Therefore, the total number of possible outcomes for the first three digits is calculated as 10 * 10 * 10 = 1000.
To have the winning ticket with the first three digits in exact order, there is only one favorable outcome because the order has to be specific as per the ticket.
Thus, the number of favorable outcomes is 1.
Therefore, the probability of a ticket holder winning with the first three digits in exact order is 1/1000 or 0.001 (0.1%).
Assuming a ticket has four digits, would like to know if the last digit must match or not.
In any case, matching each of the first three digits has a probability of 1/10.
Matching all three is a three-step experiment, so multiplication rule applies, or
P(123)=P(1)*P(2)*P(3)=1/10 * 1/10 * 1/10 =1/1000
I am sure you are able to take it from here if four digits are required to match to win.