A jar contains 5 red marbles, numbered 1 to 5, and 12 blue marbles numbered 1 to 12.
a) A marble is chosen at random. If you're told the marble is red, what is the probability that it has the number 3 on it?
b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 1 on it, what is the probability the marble is red?
To answer both questions, we need to calculate the probability based on the provided information.
a) A marble is chosen at random, and we are told that the marble is red. We need to find the probability that it has the number 3 on it.
There are a total of 5 red marbles numbered 1 to 5, so the probability of selecting a red marble is 5/17 (since there are a total of 17 marbles in the jar).
Out of the 5 red marbles, only one of them has the number 3 on it. So the probability of selecting a red marble with the number 3 on it is 1/5.
Therefore, the probability that the chosen red marble has the number 3 on it is (1/5)/(5/17) = 17/25.
b) The first marble is replaced, and another marble is chosen at random. We are told that the marble has the number 1 on it, and we need to find the probability that the marble is red.
Since the first marble is replaced, the total number of marbles remains the same - 17.
Again, there are a total of 5 red marbles and 12 blue marbles. So the probability of selecting a red marble is 5/17.
However, since we are told that the marble has the number 1 on it, we need to consider only the marbles with number 1.
There is only 1 red marble with the number 1 and 1 blue marble with the number 1.
So the probability of selecting a red marble given that it has the number 1 on it is 1/2.
Therefore, the probability that the chosen marble is red given that it has the number 1 on it is 1/2.