To solve the problem of finding the probability that a girl is selected to do both jobs on Monday, let's break it down step by step.
1. Understand the Problem:
- We need to find the probability that a girl is selected to do both jobs.
- The probability a girl is selected for the first job and the probability she is selected for the second job, given that a girl has already been selected for the first job, are required.
2. Set the Probabilities:
- Let’s say the probability that a girl is selected for the first job is [tex]\(\frac{3}{5}\)[/tex].
- Given that a girl has been selected for the first job, the probability that a girl is selected for the second job is [tex]\(\frac{3}{5}\)[/tex].
3. Multiply the Probabilities:
- The probability of both independent events happening (a girl selected for the first job and then for the second job) is the product of their individual probabilities:
[tex]\[
\text{Combined Probability} = \left(\frac{3}{5}\right) \times \left(\frac{3}{5}\right)
\][/tex]
Compute this:
[tex]\[
\left(\frac{3}{5}\right) \times \left(\frac{3}{5}\right) = \frac{3 \times 3}{5 \times 5} = \frac{9}{25}
\][/tex]
4. Convert to Decimal:
- To be sure about the equivalence and correctness, we note that [tex]\(\frac{9}{25}\)[/tex] equals 0.36 as a decimal.
Comparing the given options:
- The first option is [tex]\(\frac{3}{5}\)[/tex], which is 0.60.
- The second option is [tex]\(\frac{3}{38}\)[/tex], which is a lot less than 0.36.
- The third option is [tex]\(\frac{107}{190}\)[/tex], approximately 0.563.
- The fourth option is [tex]\(\frac{9}{100}\)[/tex], which is 0.09.
None of these options match [tex]\(\frac{9}{25}\)[/tex] directly in fractional form except for the equivalent decimal form in the solution process.
Therefore, the correct choice given for a girl to be selected for both jobs on Monday is most closely represented by:
[tex]\(\boxed{\frac{9}{25} = 0.36}\)[/tex] which was deduced but not directly given in provided multiple choices.
