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A bag contains hair ribbons for a spirit rally. The bag contains 8 black ribbons and 12 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that both Lila and Jessica select a black ribbon? Express your answer as a fraction in simplest form.

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Answer:

[tex]\boxed{\sf \dfrac{14}{95}}[/tex]

Explanation:

Black ribbons = 8 ribbons

Green ribbons = 12 ribbons

Total ribbons: 12 + 8 = 20 ribbons

[tex]\sf Probability = \dfrac{Favorable \ Outcomes}{Total \ Possible \ Outcomes}[/tex]

For Lila:

[tex]\sf Lila \ picks \ black \ : \ \dfrac{8}{20}[/tex]

Left black ribbons: 8 - 1 = 7 black ribbons

Left total ribbons: 20 -1 = 19 total ribbons

For Jessica:

[tex]\sf Jessica \ picks \ black \ : \ \dfrac{7}{19}[/tex]

Probability that they both pick black ribbons:

[tex]\sf \rightarrow \dfrac{8}{20} \ x \ \dfrac{7}{19}[/tex]

[tex]\sf \rightarrow \dfrac{14}{95}[/tex]

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