Question

John had a bag of marbles as shown below.

What is the probability that John selects a green marble, replaces it, and then selects a
green marble?
3 green marbles
4 blue marbles
2 red marbles
1 yellow marble

A.9/100
B.1/ 10
C.1/15
D.1/50

Answer 1

`\sf A) \quad (9)/(100)`

Explanation:

Given:

• 3 green marbles
• 4 blue marbles
• 2 red marbles
• 1 yellow marble

Total number of marbles = 3 + 4 + 2 + 1 = 10

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

Probability of selecting a green marble on first pick:

`\implies \sf P(green\:marble)=(3)/(10)`

Probability of selecting a green marble on second pick:

`\implies \sf P(green\:marble)=(3)/(10)`

(as the 1st pick was replaced)

Therefore,

`\implies \textsf{P(green marble) and P(green marble)} \sf =(3)/(10) * (3)/(10)=(9)/(100)`