Question

A jar contains 4 red marbles, numbered 1 to 4, and 9 blue marbles numbered 1 to 9.b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 5 on it, what is the probability the marble is blue?

Answer 1

ANSWER:

0.11

STEP-BY-STEP EXPLANATION:

Numbers of red marbles = 4

Numbers of blue marbles = 9

Total marbles = 14

P (blue) = 9/14

P (number 5) = 2/14 = 1/7

P(blue and number 5) = 1/14 (there is 1 marble that is blue and has the number 5 on it)

We have to find P (number 5 | blue)

$\begin{gathered} P(\text{ number 5| blue) }=\frac{\text{ P(blue and number 5) }}{\text{ P(blue)}}=\frac{\frac{1}{14}}{\frac{9}{14}} \\ P(\text{ number 5| blue) }=\frac{1\cdot14}{14\cdot9} \\ P(\text{ number 5| blue) }=\frac{1}{9} \end{gathered}$

The probability is 0.11