Answer :
To determine the probability that a randomly selected ball from the Bingo game has a letter [tex]\(B\)[/tex] or [tex]\(O\)[/tex], we can use the probabilities given in the table.
Here's the step-by-step solution:
1. Identify the given probabilities:
- Probability of selecting a ball with the letter [tex]\(B\)[/tex] is [tex]\(0.16\)[/tex].
- Probability of selecting a ball with the letter [tex]\(O\)[/tex] is [tex]\(0.18\)[/tex].
2. Use the rule of addition:
The rule of addition for probabilities states that if we want to find the probability of one of several mutually exclusive events happening, we simply add their probabilities. Since [tex]\(B\)[/tex] and [tex]\(O\)[/tex] are mutually exclusive (a ball cannot be labeled with both letters), we add their probabilities.
3. Calculate the combined probability:
[tex]\[ P(\text{B or O}) = P(B) + P(O) \][/tex]
Substituting in the values:
[tex]\[ P(\text{B or O}) = 0.16 + 0.18 \][/tex]
4. Add the probabilities:
[tex]\[ P(\text{B or O}) = 0.34 \][/tex]
Thus, the probability that a randomly selected ball has a letter [tex]\(B\)[/tex] or [tex]\(O\)[/tex] is
[tex]\[ P(\text{B or O}) = 0.34. \][/tex]
Now, to ensure accuracy and confirm the computational process:
The sum [tex]\(0.16 + 0.18\)[/tex] mathematically yields [tex]\(0.33999999999999997\)[/tex] due to floating-point representation in calculations, and when rounded to a suitable precision, it becomes [tex]\(0.34\)[/tex]. Hence, the accurate probability is:
[tex]\[ P(\text{B or O}) = 0.34. \][/tex]
Here's the step-by-step solution:
1. Identify the given probabilities:
- Probability of selecting a ball with the letter [tex]\(B\)[/tex] is [tex]\(0.16\)[/tex].
- Probability of selecting a ball with the letter [tex]\(O\)[/tex] is [tex]\(0.18\)[/tex].
2. Use the rule of addition:
The rule of addition for probabilities states that if we want to find the probability of one of several mutually exclusive events happening, we simply add their probabilities. Since [tex]\(B\)[/tex] and [tex]\(O\)[/tex] are mutually exclusive (a ball cannot be labeled with both letters), we add their probabilities.
3. Calculate the combined probability:
[tex]\[ P(\text{B or O}) = P(B) + P(O) \][/tex]
Substituting in the values:
[tex]\[ P(\text{B or O}) = 0.16 + 0.18 \][/tex]
4. Add the probabilities:
[tex]\[ P(\text{B or O}) = 0.34 \][/tex]
Thus, the probability that a randomly selected ball has a letter [tex]\(B\)[/tex] or [tex]\(O\)[/tex] is
[tex]\[ P(\text{B or O}) = 0.34. \][/tex]
Now, to ensure accuracy and confirm the computational process:
The sum [tex]\(0.16 + 0.18\)[/tex] mathematically yields [tex]\(0.33999999999999997\)[/tex] due to floating-point representation in calculations, and when rounded to a suitable precision, it becomes [tex]\(0.34\)[/tex]. Hence, the accurate probability is:
[tex]\[ P(\text{B or O}) = 0.34. \][/tex]
