The table below gives the probability density of balls remaining for a game of Bingo.
| Letter | B | I | N | G | O |
| :----- | :--- | :--- | :--- | :--- | :--- |
| Probability | 0.16 | 0.22 | 0.18 | 0.26 | 0.18 |
If a ball is selected at random, what is the probability that its letter is an I or G?
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Answer (2)
The probability of selecting a ball with the letter I or G in Bingo is 0.48, or 48%. This is calculated by adding the individual probabilities of selecting I (0.22) and G (0.26). Therefore, P ( I or G ) = 0.22 + 0.26 = 0.48 .
;
The probability of selecting an 'I' is 0.22 .
The probability of selecting a 'G' is 0.26 .
Add the probabilities since the events are mutually exclusive: 0.22 + 0.26 = 0.48 .
The probability of selecting an 'I' or 'G' is 0.48 .
Explanation
Understand the problem We are given the probabilities for each letter in a Bingo game. We need to find the probability of selecting a ball with the letter I or G.
Identify given probabilities The probability of selecting a ball with the letter I is given as P ( I ) = 0.22 . The probability of selecting a ball with the letter G is given as P ( G ) = 0.26 .
Apply the addition rule for mutually exclusive events Since the events of selecting a ball with letter I and selecting a ball with letter G are mutually exclusive (a ball cannot have both letters), we can find the probability of selecting a ball with letter I or G by adding their individual probabilities: P ( I \t or G ) = P ( I ) + P ( G ) .
Calculate the combined probability Now, we substitute the given probabilities: P ( I \t or G ) = 0.22 + 0.26 = 0.48 .
State the final answer Therefore, the probability that a randomly selected ball has the letter I or G is 0.48 .
Examples
In a game of Bingo, understanding the probabilities of drawing certain letters can help players anticipate which numbers might be called. For instance, if you need either an 'I' or a 'G' to win, calculating the combined probability helps you assess your chances. If the probability of 'I' is 0.22 and 'G' is 0.26, then your chance of getting either is 0.48, or 48%. This kind of probability calculation is useful in many games of chance.
