Answer/Step-by-step explanation:
To find the probability of drawing 4 red marbles out of the total marbles in the bag, we can calculate it step by step:
1. **Total number of marbles**: There are 5 red marbles, 10 white marbles, and 9 blue marbles, making a total of 24 marbles in the bag.
2. **Probability of drawing the first red marble**: The probability of drawing a red marble on the first draw is \( \frac{5}{24} \) since there are 5 red marbles out of 24 total marbles.
3. **Probability of drawing the second red marble**: After drawing one red marble, there are 4 red marbles left and 23 total marbles remaining. So, the probability of drawing a second red marble is \( \frac{4}{23} \).
4. **Probability of drawing the third red marble**: With 3 red marbles left and 22 total marbles after drawing two red marbles, the probability of drawing a third red marble is \( \frac{3}{22} \).
5. **Probability of drawing the fourth red marble**: Finally, with 2 red marbles and 21 total marbles left, the probability of drawing the fourth red marble is \( \frac{2}{21} \).
6. **Multiply the probabilities**: To find the probability of all 4 marbles being red, we multiply the probabilities of each draw: \( \frac{5}{24} \times \frac{4}{23} \times \frac{3}{22} \times \frac{2}{21} \).
7. **Calculate the final probability**: Multiply the fractions and simplify the result to get the final probability.
