8.9 Box
8.9.1 Box Problem #01
In a box, there are 5 blue marbles, 7 green marbles, and 8 yellow marbles. If two marbles are randomly selected, what is the probability that both will be green or yellow, if taken
with replacement
without replacement
- Correct or not: \(\frac{^7C_2}{^{20}C_2}+\frac{^8C_2}{^{20}C_2}\)
- \(\frac{^7C_1 \times ^7C_1}{^{20}C_1 \times ^{20}C_1}+\frac{^8C_1 \times ^8C_1}{^{20}C_1 \times ^{20}C_1}\)
- Without replacement: \(\frac{^7C_1 \times ^6C_1}{^{20}C_1 \times ^{20}C_1}+\frac{^8C_1 \times ^7C_1}{^{20}C_1 \times ^{20}C_1}\)
8.9.2 Box Problem #02
There are some balls in a box as below
| Color | # Balls |
|---|---|
| White | 3 |
| Black | 6 |
| Red | 7 |
| Green | 5 |
| Yellow | 4 |
| Violet | 9 |
| Blue | 8 |
If three balls are drawn at random, what is the probability there are all red or green?
- \(\frac{^7C_3}{^{42}C_3}+\frac{^5C_3}{^{42}C_3}\)
- 0.039
8.9.3 Box Problem #02
There are 9 red and 7 white balls in a box. 6 balls are picked randomly. What is the probability that 3 balls are red and 3 balls are white?
Which one is the answer?
- \(\frac{^9C_3 \times ^7C_3}{^{16}C_6}\)
- \(\frac{^9C_3}{^{16}C_3} \times \frac{^7C_3}{^{16}C_3}\)
- \(\frac{^9C_3}{^{16}C_3} + \frac{^7C_3}{^{16}C_3}\)
- \(\frac{^9C_3}{^{16}C_6} \times \frac{^7C_3}{^{16}C_6}\)
- Whatever we draw together will be in \(r\) in \(^nC_r\)
- Answer: \(\frac{^9C_3 \times ^7C_3}{^{16}C_6}\)=0.367