Question

An jar contains 5 green marbles and 9 purple marbles. A marble is drawn and dropped back into the jar. Both marbles are green. If another marble is drawn, what is the probability that it will be green?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for Probability

$Probability=\frac{number\text{ of required events}}{number\text{ of total possible outcomes}}$

STEP 2: Write the different outcomes

$\begin{gathered} n(green)=5 \\ n(purple)=9 \\ n(Total)=5+9=14 \end{gathered}$

STEP 3: Find the probability that the third marble drawn is green

Since it can be seen from the question that the selection was done with replacement, this means that the sample space of 5 green marbles and 9 purple marbles are not affected. The probability of this outcome using the formula in step 1 will be given by:

$\begin{gathered} P(green)=\frac{n(green)}{n(Total)} \\ \\ P(green)=\frac{5}{14} \end{gathered}$

The probability that it will be green is 5/14