Question

Suppose a jar contains 18 red marbles and 10 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round to at least 2 decimal places______.

Answer 1

Given

18 red marbles

10 blue marbles

A total of 28 marbles

With replacement

$\begin{gathered} P(RR)=\frac{\text{total number of red marbles}}{\text{total number of marbles}}\cdot\frac{\text{total number of red marbles}}{\text{total number of marbles}} \\ P(RR)=\frac{18}{28}\cdot\frac{18}{28} \\ P(RR)=\frac{324}{784} \\ P(RR)=0.413265 \end{gathered}$

Rounding to the nearest 2 decimal places, the probability with replacement is 0.41.

Without replacement

$\begin{gathered} P(RR)=\frac{\text{total number of red marbles}}{\text{total number of marbles}}\cdot\frac{\text{total number of red marbles left}}{\text{total number of marbles left}} \\ P(RR)=\frac{18}{28}\cdot\frac{17}{27} \\ P(RR)=\frac{306}{756} \\ P(RR)=0.40476 \end{gathered}$

Rounding to the nearest 2 decimal places, the probability is 0.40.