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When playing bingo, 75 balls are placed in a bin and balls are selected at random. Each ball is marked with a letter and number as indicated in the chart below. For example, there are balls marked B1, B2, up to B15; I16, I17, up to 30; and so on. Assume one bingo ball is selected at random.

[tex]\[
\frac{B}{1-15} \quad \frac{I}{16-30} \quad \frac{N}{31-45} \quad \frac{G}{46-60} \quad \frac{O}{61-75}
\][/tex]

What is the probability it has the letters B or G on it?

(Type a fraction. Simplify your answer.)



Answer :

GinnyAnswer
To determine the probability of selecting a bingo ball that has either the letter B or G on it, follow these steps:

1. Analyze the Distribution of Balls:
Each letter (B, I, N, G, and O) covers a specific range of 15 balls each.
- B covers numbers 1 to 15 (15 balls)
- I covers numbers 16 to 30 (15 balls)
- N covers numbers 31 to 45 (15 balls)
- G covers numbers 46 to 60 (15 balls)
- O covers numbers 61 to 75 (15 balls)

2. Total Number of Balls:
The total number of bingo balls is 75.

3. Determine the Desired Outcomes:
We are interested in balls marked with the letters B or G.
- The number of B balls is 15.
- The number of G balls is 15.

4. Calculate the Total Number of Desired Balls:
[tex]\[ \text{Total desired balls} = \text{Number of B balls} + \text{Number of G balls} = 15 + 15 = 30 \][/tex]

5. Calculate the Probability:
The probability is given by the ratio of the number of desired outcomes to the total number of possible outcomes.
[tex]\[ \text{Probability} = \frac{\text{Total desired balls}}{\text{Total number of balls}} = \frac{30}{75} \][/tex]

6. Simplify the Fraction:
Simplify [tex]\(\frac{30}{75}\)[/tex] by finding the greatest common divisor of 30 and 75, which is 15.
[tex]\[ \frac{30}{75} = \frac{30 \div 15}{75 \div 15} = \frac{2}{5} \][/tex]

Therefore, the simplified probability that a randomly selected bingo ball has the letters B or G on it is:
[tex]\[ \boxed{\frac{2}{5}} \][/tex]

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