Pick 4 The Illinois Lottery’s PICK 4 game is similar to PICK 3, except a player must match a sequence of four repeatable numbers, ranging from 0 to 9, in exact order (for example, 5–8–5–1). With a single ticket, what is the probability of matching the four winning numbers?

Verified step by step guidance

1. Understand the problem: You need to find the probability of matching a specific sequence of four numbers, each ranging from 0 to 9, in the exact order they are drawn.
2. Determine the total number of possible outcomes: Since each of the 4 positions can be any digit from 0 to 9, and digits can repeat, the total number of possible sequences is calculated by multiplying the number of choices for each position.
3. Express the total number of possible sequences mathematically as \$10 \times 10 \times 10 \times 10 = 10^4$.
4. Recognize that there is only one winning sequence that matches the exact order of the drawn numbers.
5. Calculate the probability of winning by dividing the number of winning sequences (1) by the total number of possible sequences, which is \(\frac{1}{10^4}\).

Key Concepts

Sample Space in Probability

The sample space is the set of all possible outcomes in a probability experiment. For the PICK 4 game, each digit ranges from 0 to 9, and since there are four digits, the total number of possible sequences is 10^4 = 10,000. Understanding the sample space helps determine the total number of possible tickets.

Probability of a Single Event

The probability of a single event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, matching the exact four-digit sequence is one specific outcome, so the probability is 1 divided by the total number of sequences.

Independent and Repeatable Outcomes

Each digit in the sequence is chosen independently and can repeat digits (0-9). This means the outcome of one digit does not affect the others, and digits can appear multiple times, which influences the total number of possible sequences and the calculation of probability.