Question

a jar contains 6 red marbles, numbered 1 to 6, and 11 blue marbles numbered 1 to 11.
a) a marble is chosen at random. if youre told the marble is blue, what is the probability that it has the number 4 on it?
b) the first marble is replaced, and another marble is chosen at random. if youre told the marble has the number 1 on it, what is the probability the marble is blue?

Explanation:

Step1: Identify relevant counts for part a

There are 11 blue marbles, and 1 blue marble has number 4.

Step2: Calculate probability for part a

The probability formula for conditional - probability in this case is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability that a blue marble has number 4 is $\frac{1}{11}$.

Step3: Identify relevant counts for part b

There are 6 red marbles and 11 blue marbles. Among them, 1 red marble has number 1 and 1 blue marble has number 1, so there are a total of $1 + 1=2$ marbles with number 1, and 1 of them is blue.

Step4: Calculate probability for part b

Using the probability formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$, the probability that a marble with number 1 is blue is $\frac{1}{2}$.

Answer:

a) $\frac{1}{11}$
b) $\frac{1}{2}$