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.
To find the probability that the marble drawn is blue or even-numbered, we need to determine the total number of favorable outcomes (blue marbles or even-numbered marbles) and the total number of possible outcomes.
1. Determine the total number of favorable outcomes:
- Blue marbles: There are 7 blue marbles in the jar.
- Even-numbered marbles: There are 4 even-numbered marbles (2, 4, 6, and 8) in the jar.
To avoid double-counting the blue marbles that are also even-numbered (2 and 6), we need to subtract those from the total.
- Total number of favorable outcomes = 7 (blue marbles) + 4 (even-numbered marbles) - 2 (blue and even-numbered marbles) = 9 favorable outcomes.
2. Determine the total number of possible outcomes:
- Total number of marbles in the jar = 9 red marbles + 7 blue marbles = 16 marbles.
3. Calculate the probability:
- Probability = favorable outcomes / total outcomes
- Probability = 9 / 16 ≈ 0.5625
Therefore, the probability that the marble drawn from the jar is blue or even-numbered is approximately 0.5625 or 56.25%.
To find the probability that the marble drawn is blue or even-numbered, we need to calculate the favorable outcomes and the total outcomes.
Step 1: Calculate the favorable outcomes
- There are 7 blue marbles.
- Out of the 16 marbles in total, half of them are even-numbered (2, 4, 6).
- Therefore, the favorable outcomes are 7 blue marbles + 3 even-numbered marbles = 10.
Step 2: Calculate the total outcomes
- There are a total of 16 marbles in the jar.
Step 3: Calculate the probability
- The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes.
- Probability = Favorable outcomes / Total outcomes
- Probability = 10 / 16
Simplifying the probability:
- 10 / 16 can be simplified as 5 / 8.
Therefore, the probability that the marble drawn is blue or even-numbered is 5/8.