Let's solve the problem step-by-step:
1. Total number of shirts: There are 12 shirts in total.
[tex]\[
\text{Total shirts} = 12
\][/tex]
2. Number of blue shirts: Out of these, 5 shirts are blue.
[tex]\[
\text{Number of blue shirts} = 5
\][/tex]
3. Number of blue shirts that fit well: Out of the 5 blue shirts, 4 fit well.
[tex]\[
\text{Blue shirts that fit well} = 4
\][/tex]
4. Number of green shirts: There are also 7 green shirts.
[tex]\[
\text{Number of green shirts} = 7
\][/tex]
5. Number of green shirts that fit well: Out of the 7 green shirts, only 1 fits well.
[tex]\[
\text{Green shirts that fit well} = 1
\][/tex]
6. Calculate the number of shirts that are too big:
- The shirts that fit well are the 4 blue shirts and the 1 green shirt.
- This gives us a total of 5 shirts that fit well.
[tex]\[
\text{Total shirts that fit well} = 4 + 1 = 5
\][/tex]
- Therefore, the number of shirts that are too big is the total number of shirts minus the number of shirts that fit well.
[tex]\[
\text{Too big shirts} = 12 - 5 = 7
\][/tex]
7. Calculate the favorable outcomes:
- A shirt is considered favorable if it is blue or too big.
- The number of blue shirts is 5.
- The number of too big shirts is 7.
[tex]\[
\text{Favorable shirts} = \text{Number of blue shirts} + \text{Number of too big shirts} = 5 + 7 = 12
\][/tex]
8. Calculate the probability of a shirt being blue or too big:
- The probability is the number of favorable outcomes divided by the total number of outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable shirts}}{\text{Total number of shirts}} = \frac{12}{12} = 1
\][/tex]
Thus, the probability of randomly selecting a shirt that is either blue or too big is [tex]\(1\)[/tex].
Hence, the correct answer is [tex]\(\boxed{1.0}\)[/tex].
