A jar contains 9 red marbles numbered 1 to 9 and 7 blue marbles numbered 1 to 7. A marble is drawn at random from the jar. Find the probability that the marble is blue or even-numbered.


I had 1/7

P(Blue) = 7/16

P(Even) = 7/16

Either-or probabilities are found by adding the individual probabilities.

To find the probability of drawing a blue or even-numbered marble, we need to calculate the number of favorable outcomes (blue marbles and even-numbered marbles) and divide it by the total number of possible outcomes.

Favorable outcomes:
- Blue marbles: There are 7 blue marbles in the jar.
- Even-numbered marbles: There are 9 marbles in total that are either red or blue and numbered 2, 4, 6, or 8.

Total possible outcomes:
- Total marbles in the jar: There are 9 red marbles and 7 blue marbles, so a total of 9 + 7 = 16 marbles.

Now, we can calculate the probability:

P(blue or even-numbered) = (Number of favorable outcomes) / (Total possible outcomes)
= (7 + 4) / 16
= 11 / 16

Therefore, the probability that the marble drawn is blue or even-numbered is 11/16.

To find the probability that the marble drawn is blue or even-numbered, we need to first determine the number of blue marbles and the number of even-numbered marbles.

We know that there are 7 blue marbles numbered 1 to 7, so the number of blue marbles is 7.

For the even-numbered marbles, we consider the numbers 2, 4, 6, and 8. These are the even numbers between 1 and 9 (since there are 9 marbles numbered 1 to 9). So the number of even-numbered marbles is 4.

Now, to calculate the probability, we use the formula:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

The favorable outcomes in this case are the blue or even-numbered marbles, which is the union of the blue marbles and the even-numbered marbles. Since there is no overlap between these two sets, the number of favorable outcomes is the sum of the number of blue marbles and the number of even-numbered marbles. Therefore, the number of favorable outcomes is 7 + 4 = 11.

The total number of possible outcomes is the total number of marbles in the jar, which is 9 (red marbles) + 7 (blue marbles) = 16.

Plugging these values into the formula:

Probability = 11 / 16.

Simplifying the fraction if possible, we have the final answer:

Probability = 11/16.

Thus, the probability that the marble drawn is blue or even-numbered is 11/16.