A jar contains 5 red marbles, numbered 1 to 5, and 11 blue marbles numbered 1 to 11.

a) A marble is chosen at random. If you're told the marble is red, what is the probability that it has the number 2 on it?
b)The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 7 on it, what is the probability the marble is red?

a) Well, if you're told that the marble is red, it narrows down the options. There are only 5 red marbles in total. And out of those 5, only 1 has the number 2 on it. So the probability of picking a red marble with the number 2 on it is 1/5, or in other words, one in a 2-handful of marbles.

b) Ah, the plot thickens! Now, even though we know the marble has the number 7 on it, we still need to take into account both the red and blue marbles. This time, out of the 16 total marbles (5 red and 11 blue), only 5 are red. But since we already know the marble has the number 7, which is blue, the probability of it being red is none other than a big fat zero! So, no red marbles for you this time.

a) To calculate the probability that a red marble has the number 2 on it, we need to determine the number of favorable outcomes (red marble with the number 2) and the total number of possible outcomes (all red marbles).

The number of red marbles with the number 2 is 1 (there is only one red marble with the number 2).

The total number of red marbles is 5.

Therefore, the probability that a red marble has the number 2 on it is 1/5.

b) To calculate the probability that a marble is red given that it has the number 7 on it, we need to determine the number of favorable outcomes (red marbles with the number 7) and the total number of possible outcomes (all marbles with the number 7).

The number of red marbles with the number 7 is 0 (there are no red marbles with the number 7).

The total number of marbles with the number 7 is 2 (1 red marble with the number 7 and 1 blue marble with the number 7).

Therefore, the probability that the marble is red given that it has the number 7 on it is 0/2 or 0.

a) To find the probability that a red marble has the number 2 on it, we need to determine the ratio of favorable outcomes (red marble with number 2) to the total number of outcomes (all red marbles).

Step 1: Find the total number of red marbles. In this case, there are 5 red marbles.

Step 2: Find the number of red marbles with the number 2. As there is only 1 red marble with the number 2, the favorable outcome is 1.

Step 3: Find the probability. The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the probability is 1/5, or 0.2, which can also be expressed as 20%.

So, the probability that a red marble chosen at random has the number 2 on it is 0.2 or 20%.

b) Similarly, to find the probability that a marble is red given that it has the number 7 on it, we need to determine the ratio of favorable outcomes (red marbles) to the total number of outcomes (marbles with the number 7).

Step 1: Find the total number of marbles with the number 7. In this case, there is only 1 marble with the number 7.

Step 2: Find the number of red marbles. There are 5 red marbles in total.

Step 3: Find the probability. The probability is calculated by dividing the number of favorable outcomes (red marbles) by the total number of outcomes (marbles with the number 7). In this case, the probability is 5/1, or 5, which can also be expressed as 500%.

However, probabilities should always be between 0 and 1, so the maximum probability is 1. This means that the probability of a marble being red, given that it has the number 7 on it, is 1 or 100%.

Therefore, the probability that the second marble is red, given that it has the number 7 on it, is 1 or 100%.

1/5

zero