At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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]