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The table below gives the probability density of balls remaining for a game of Bingo.

\begin{tabular}{|c|c|c|c|c|c|}
\hline
Letter & B & I & N & G & O \\
\hline
Probability & 0.16 & 0.22 & 0.18 & 0.26 & 0.18 \\
\hline
\end{tabular}

If a ball is selected at random, what is the probability that its letter is a [tex]$B$[/tex] or [tex]$O$[/tex]?
[tex]\[ P = ? \][/tex]

Sagot :

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]
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