Sure, let's tackle this problem step-by-step.
1. Given Data:
We have the probabilities for picking a ball with each letter from the table:
- P(B) = 0.16
- P(I) = 0.22
- P(N) = 0.18
- P(G) = 0.26
- P(O) = 0.18
2. Question Requirement:
We need to find the probability that a randomly selected ball is either an I or an O.
3. Identify Probabilities:
From the given data:
- Probability of selecting a ball with letter I = P(I) = 0.22
- Probability of selecting a ball with letter O = P(O) = 0.18
4. Combine Probabilities:
The events "selecting a ball with letter I" and "selecting a ball with letter O" are mutually exclusive events (cannot happen at the same time). Thus, the total probability is given by the sum of individual probabilities:
[tex]\[
P(\text{I or O}) = P(\text{I}) + P(\text{O})
\][/tex]
5. Calculation:
Substituting the values from our data:
[tex]\[
P(\text{I or O}) = 0.22 + 0.18 = 0.40
\][/tex]
So, the probability that a randomly selected ball has a letter I or O is:
[tex]\[
P = 0.40
\][/tex]
In two digit form:
[tex]\[
P = 0.40
\][/tex]
Thus, [tex]\( P = 0.40 \)[/tex].
