Lingo
In the gameshow Lingo, the team that correctly guesses a mystery word gets a chance to pull two Lingo balls from a bin. Balls in the bin are labeled with numbers that match the numbers still on the team's Lingo board. There are also three prize balls and three red "stopper" balls in the bin. If a stopper ball is drawn first, the team loses its second draw. To form a Lingo, the team needs five numbers in a row—vertically, horizontally, or diagonally. Consider the sample Lingo board below for a team that has just guessed a mystery word.

a. What is the probability that the first ball selected is on the Lingo board?

Verified step by step guidance

1. Step 1: Identify the total number of balls in the bin. This includes all the numbers still on the team's Lingo board, plus the three prize balls and the three red stopper balls.
2. Step 2: Count the number of green-highlighted numbers on the Lingo board, as these represent the numbers still on the board and thus the balls that match the board.
3. Step 3: Calculate the total number of balls by adding the count of green numbers, the 3 prize balls, and the 3 stopper balls.
4. Step 4: The probability that the first ball selected is on the Lingo board is the ratio of the number of green balls (numbers on the board) to the total number of balls in the bin.
5. Step 5: Express this probability as a fraction or decimal using the formula: \(\text{Probability} = \frac{\text{Number of green balls}}{\text{Total number of balls}}\).

Key Concepts

Probability

Probability measures the likelihood of an event occurring, expressed as a ratio of favorable outcomes to total possible outcomes. It ranges from 0 (impossible event) to 1 (certain event). In this question, probability helps determine the chance of drawing a ball that matches a number on the Lingo board.

Sample Space and Favorable Outcomes

The sample space is the set of all possible outcomes in an experiment, while favorable outcomes are those that meet the event criteria. Here, the sample space includes all balls in the bin, and favorable outcomes are balls labeled with numbers currently on the Lingo board.

Counting and Identifying Relevant Elements

Accurately counting the number of balls on the Lingo board and the total balls in the bin is essential. This involves identifying which numbers are still active on the board (highlighted in green) and understanding the total composition of the bin, including prize and stopper balls.