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Sagot :
EXPLANATION:
Given;
We are told that a bag contains the following;
[tex]\begin{gathered} Black\text{ }ribbons=18 \\ \\ Green\text{ }ribbons=2 \\ \\ Total=20 \end{gathered}[/tex]Lila selects a ribbon at random and then Jessica selects a ribbon at random from the remaining ones.
Required;
Calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon.
Step-by-step solution;
The probability of an event is calculated by the formula given below;
[tex]P[Event]=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}[/tex]For Lila to select a black ribbon, we have;
[tex]\begin{gathered} P[black]=\frac{18}{20} \\ \\ P[black]=\frac{9}{10} \end{gathered}[/tex]Now we have 19 ribbons left, note that Jessica had to select from the remaining ribbons.
For Jessica to select a green ribbon, we have;
[tex]P[green]=\frac{2}{19}[/tex]Next to calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon we have a product of probabilities;
[tex]\begin{gathered} P[black]\text{ }and\text{ }P[green]=\frac{9}{10}\times\frac{2}{19} \\ \\ P[black]\text{ }and\text{ }P[green]=\frac{9}{95} \end{gathered}[/tex]Therefore,
ANSWER:
The probability that Lila selects a black ribbon and Jessica selects a green ribbon is,
[tex]\frac{9}{95}[/tex]
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