Question

A jar contains 5 red marbles, numbered 1 to 5, and 11 blue marbles numbered 1 to 11. b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 9 on it, what is the probability the marble is blue?

Answer 1

It is given that a jar contains 5 red marbles, numbered 1 to 5, and 11 blue marbles numbered 1 to 11. One marble is chosen at random. If we are told that the marble has the number 9 on it, we have to find the probability that the marble is blue.

We know, Probability of any event = (Number of favorable outcomes)/(Total number of possible outcomes).

It is told that the marble has number 9 on it. There are 11 blue marbles numbered 1 to 11. The red marbles are numbered 1 to 5. Thus, the number 9 comes only in case of blue marbles. There are 11 blue marbles. Thus, total number of possible outcomes = 11.

Now, among these 11 marbles, only one marble is numbered 9. Thus, number of favorable outcomes = 1.

Thus, required probability = 1/11 = 0.0909(rounded up to four decimal places).

Thus, if the marble has number 9 on it, the probability that the marble is blue = 0.0909 .