Question

Playing “Pick $4$” The Pick $4$games in many state lotteries announce a four-digit winning number each day. You can think of the winning number as a four-digit group from a table of random digits. You win (or share) the jackpot if your choice matches the winning number. The winnings are divided among all players who matched the winning number. That suggests a way to get an edge.

(a) The winning number might be, for example, either $2873$or $9999$. Explain why these two outcomes have exactly the same probability.

(b) If you asked many people whether 2873 or $9999$ is more likely to be the randomly chosen winning number, most would favor one of them. Use the information in this section to say which one and to explain why. How might this affect the four-digit number you would choose?

Short answer

Part (a) the same probability is a characteristic that describes a group of occurrences that all have the same chance of happening.

Part (b) Using the information, the winning number will be $2873$

Step-by-step solution

Part (a) Step 1. Given Information 

Every day, a four-digit winning number is announced in the Pick $4$games of various state lotteries. The winning number can be thought of as a four-digit group selected from a table of random digits. If your selection matches the winning number, you win (or share) the jackpot. All players that matched the winning number share the prize pool. That offers a strategy for gaining an advantage.

Part (a) Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$ (happens frequently) (always occurs).

Part (a) Step 3. Explanation  

For example, the winning numbers may be $2873$or $9999$Both of these options are assumed to have the same probability. As a result, these two numbers have the same probability because each of them is one of $10,000$four-digit numbers ranging from $0000$to $9999$, As a result, we can claim that both have the same probability.

Part (b) Step 1. Explanation  

Using the evidence presented in this section, we can conclude that most people would consider $2873$to be the more likely number since they believe the number $9$to appear four times in a row is unlikely. However, the digits $2,8,7,4$ are equally as likely to appear in that same order. Using the information, the winning number is$2873$