Question

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

Answer 1

8/121

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

Answer 2

`\sf (8)/(121)`

Explanation:

Given:

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

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

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

`\sf \implies P(mechanical\:pencil)=(2)/(11)`

As the pencil is replaced,

`\sf \implies P(colored\:pencil)=(4)/(11)`

`\begin{aligned}\sf \implies P(mechanical\:pencil)\:and\:P(colored\:pencil) &= \sf (2)/(11) * (4)/(11)\\\\ & \sf =(8)/(121)\end{aligned}`