Final answer:
The probabilities for drawing a red marble, an odd numbered marble, a red or odd numbered marble, and a blue or even numbered marble from the jar are 5/8, 1/2, 13/16, and 11/16 respectively.
Step-by-step explanation:
The student has asked about finding the probability of selecting a marble with certain characteristics from a jar. The total number of marbles in the jar is 16 (10 red + 6 blue). Here are the steps to find each probability:
- The marble is red: There are 10 red marbles out of 16 total marbles. The probability is therefore 10/16, which simplifies to 5/8.
- Marble is odd numbered: There are 5 odd numbered red marbles (1, 3, 5, 7, 9) and 3 odd numbered blue marbles (1, 3, 5), making a total of 8 odd numbered marbles. The probability is 8/16, or 1/2.
- Marble is red or odd numbered: The event that a marble is red or odd numbered includes all red marbles plus the odd numbered blue marbles not already counted in the red set. This gives us 10 red + 3 odd blue - 0 overlapping (since all red marbles are included) = 13. The probability is then 13/16.
- Marble is blue or even numbered: To find this probability, we need to count the blue marbles (6) and even numbered marbles not already counted as blue. Since the even numbered marbles are 2, 4, 6, 8, and 10 for red and 2, 4, 6 for blue, we only add the even numbered red marbles (5). This results in 6 blue + 5 even red = 11. The probability is then 11/16.
Calculating these probabilities involves identifying all the cases that satisfy the condition and dividing it by the total number of possible outcomes, which in this case is 16. This is a basic example of using combinatorics and probability theory in mathematics.