Binomial Distribution:

Binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

Solution:

The total number of ways to draw 4 cards from 9 cards with replacement is 9^4.

The number of ways to draw 4 cards from 9 cards with replacement where none of the cards is 1 is 8^4.

Therefore, the probability of drawing 4 cards from 9 cards with replacement where none of the cards is 1 is:

P = 8^4/9^4

P = 0.43046721

Explanation:

- Binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.
- In this problem, the fixed number of independent trials is 4, and the probability of success (drawing a card that is not 1) is 8/9, since there are 8 cards that are not 1 out of a total of 9 cards.
- The total number of ways to draw 4 cards from 9 cards with replacement is 9^4, since there are 9 choices for each of the 4 draws.
- The number of ways to draw 4 cards from 9 cards with replacement where none of the cards is 1 is 8^4, since there are 8 choices for each of the 4 draws.
- Therefore, the probability of drawing 4 cards from 9 cards with replacement where none of the cards is 1 is 8^4/9^4, which is approximately 0.43046721.