Question

a jar contains 3 red marbles, numbered 1 to 3, and 7 blue marbles numbered 1 to 7. a marble is chosen at random. give answer as a fraction.
a) if youre told the marble is red, what is the probability that it has the number 2 on it?
b) if youre told the marble has the number 1 on it, what is the probability the marble is red?

Explanation:

Step1: Identify total red marbles

There are 3 red marbles.

Step2: Calculate probability for part a

Only 1 red marble has number 2. Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{3}$.

Step3: Identify marbles with number 1

There is 1 red - numbered 1 and 1 blue - numbered 1, so 2 marbles have number 1.

Step4: Calculate probability for part b

There is 1 red marble with number 1. Probability = $\frac{1}{2}$.

Answer:

a) $\frac{1}{3}$
b) $\frac{1}{2}$