Question

sweater
sweatshirt
t-shirt
jeans
sweatpants
jeans
sweatpants
jeans
sweatpants
sneakers
sandals
sneakers
sandals
sneakers
sandals
sneakers
sandals
sneakers
sandals
sneakers
sandals
Probability of sweatshirt,
jeans, and sandals =

Answer 1

To calculate the probability of choosing a sweatshirt, jeans, and sandals from the provided list of clothing items, you first need to count the total number of items and how many of those specific items are present.

From your list, the items are:
- 1 sweater
- 1 sweatshirt
- 3 jeans
- 4 sweatpants
- 5 sneakers
- 5 sandals

### Count the total number of items:
- Total = 1 (sweater) + 1 (sweatshirt) + 3 (jeans) + 4 (sweatpants) + 5 (sneakers) + 5 (sandals) = 19 items

### Count the occurrences of the specific combination (sweatshirt, jeans, and sandals):
- Sweatshirt = 1
- Jeans = 3
- Sandals = 5

### Calculate the probability:
To find the probability of selecting one sweatshirt, one pair of jeans, and one pair of sandals, you multiply the probabilities of selecting each item:

1. Probability of selecting a sweatshirt:
- \( P(\text{sweatshirt}) = \frac{1}{19} \)

2. Probability of selecting a pair of jeans:
- \( P(\text{jeans}) = \frac{3}{19} \)

3. Probability of selecting a pair of sandals:
- \( P(\text{sandals}) = \frac{5}{19} \)

Now, multiply these probabilities together to find the joint probability:

\[
P(\text{sweatshirt, jeans, sandals}) = P(\text{sweatshirt}) \times P(\text{jeans}) \times P(\text{sandals}) = \frac{1}{19} \times \frac{3}{19} \times \frac{5}{19}
\]

\[
= \frac{15}{6859}
\]

### Final Probability:
Thus, the probability of choosing a sweatshirt, jeans, and sandals is \( \frac{15}{6859} \).