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there are 2 mechanical pencils 4 colored pencils and 5 regular pencils in the desk what is the chance of pulling a mechanical pencil out then replacing it pulling a colored pencil out

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Answer:

8/121

Step-by-step explanation:

P (mechanical pencil)

  • Number of mechanical pencils / Total number of pencils
  • 2 / 2 + 4 + 5
  • 2/11

It mentions it is replaced. Hence, original constitution of pencil is restored.

P (colored pencil)

  • Number of colored pencils / Total number of pencils
  • 4 / 2 + 4 + 5
  • 4/11

P (final) = P (mechanical pencil) × P (colored pencil)

  • 2/11 × 4/11
  • 8/121

semsee45

Answer:

[tex]\sf \dfrac{8}{121}[/tex]

Step-by-step explanation:

Given:

  • 2 mechanical pencils
  • 4 colored pencils
  • 5 regular pencils

Total number of pencils = 2 + 4 + 5 = 11

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\sf \implies P(mechanical\:pencil)=\dfrac{2}{11}[/tex]

As the pencil is replaced,

[tex]\sf \implies P(colored\:pencil)=\dfrac{4}{11}[/tex]

[tex]\begin{aligned}\sf \implies P(mechanical\:pencil)\:and\:P(colored\:pencil) &= \sf \dfrac{2}{11} \times \dfrac{4}{11}\\\\ & \sf =\dfrac{8}{121}\end{aligned}[/tex]

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