Sure, let's address each part of this question step by step.
### Die is Tossed Once
When a die is tossed once, the possible outcomes consist of all the faces of the die. Since a standard die has six faces numbered from 1 to 6, we list the outcomes as follows:
- Outcomes of tossing a die: {1, 2, 3, 4, 5, 6}
### Drawing a Ball from a Bag
If a bag contains 5 balls of different colors, and you draw one ball at random, the possible outcomes are the colors of the balls in the bag. Suppose the colors are red, blue, green, yellow, and black. The possible outcomes are:
- Outcomes of drawing a ball from the bag: {red, blue, green, yellow, black}
### Die is Thrown
When you throw a die, we can categorize the possible outcomes based on various criteria:
1. Outcomes of getting an even number
- The even numbers on a die are 2, 4, and 6.
- Even outcomes: {2, 4, 6}
2. Outcomes of getting an odd number
- The odd numbers on a die are 1, 3, and 5.
- Odd outcomes: {1, 3, 5}
3. Outcomes of getting a number that is not a prime
- The prime numbers less than or equal to 6 are 2, 3, and 5.
- The numbers that are not prime are therefore 1, 4, and 6.
- Non-prime outcomes: {1, 4, 6}
### Probability of Drawing a Specific Number from Slips
If numbers from 1 to 20 are written on separate slips and mixed thoroughly in a box, and a single slip is drawn randomly, the probability of drawing a specific number (like drawing any one particular slip) is calculated as follows:
- There are 20 slips, and only one slip can be a specific number.
- The probability [tex]\( P \)[/tex] is given by the ratio of favorable outcomes to the total number of outcomes.
[tex]\[
P(\text{drawing a specific number}) = \frac{1}{20} = 0.05
\][/tex]
- Probability of drawing a slip with a specific number: 0.05
By breaking down the problem step by step, we've listed all the required outcomes and calculated the requested probability clearly and comprehensively.
