Answer:
![\frac{1}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B24%7D)
Step-by-step explanation:
Given: A shop has
types of sweets (chocolate, taffy, gummies, and cookies),
types of snacks (chips and crackers), and
types of drinks (sodas, juice, and sports drinks). Mystery boxes are put together that randomly combine
sweet,
snack, and
drink.
To Find: probability that a mystery box contains chocolate, chips, and juice.
Solution:
Let A be the event that sweet in box is a chocolate.
B be the event that snack in box is chips.
C be the event that drink in box is juice.
shop has
types of sweets chocolate, taffy, gummies, and cookies.
![p(\text{A})=\frac{\text{desired outcomes}}{\text{possible outcome}}](https://tex.z-dn.net/?f=p%28%5Ctext%7BA%7D%29%3D%5Cfrac%7B%5Ctext%7Bdesired%20outcomes%7D%7D%7B%5Ctext%7Bpossible%20outcome%7D%7D)
![=\frac{1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D)
shop has
types of snacks chips and crackers
![p(\text{B})=\frac{\text{desired outcomes}}{\text{possible outcome}}](https://tex.z-dn.net/?f=p%28%5Ctext%7BB%7D%29%3D%5Cfrac%7B%5Ctext%7Bdesired%20outcomes%7D%7D%7B%5Ctext%7Bpossible%20outcome%7D%7D)
![=\frac{1}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B2%7D)
shop has
types of drinks sodas, juice, and sports drinks.
![p(\text{C})=\frac{\text{desired outcomes}}{\text{possible outcome}}](https://tex.z-dn.net/?f=p%28%5Ctext%7BC%7D%29%3D%5Cfrac%7B%5Ctext%7Bdesired%20outcomes%7D%7D%7B%5Ctext%7Bpossible%20outcome%7D%7D)
![=\frac{1}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%7D)
Now,
probability that box contains chocolate, chips and juice is
![p(\text{A and B and C})](https://tex.z-dn.net/?f=p%28%5Ctext%7BA%20and%20B%20and%20C%7D%29)
using multiplication rule in probability
![p(\text{A and B and C})=p(\text{A}).p(\text{B}).p(\text{C})](https://tex.z-dn.net/?f=p%28%5Ctext%7BA%20and%20B%20and%20C%7D%29%3Dp%28%5Ctext%7BA%7D%29.p%28%5Ctext%7BB%7D%29.p%28%5Ctext%7BC%7D%29)
![p(\text{A and B and C})=\frac{1}{4}\times\frac{1}{2}\times\frac{1}{3}](https://tex.z-dn.net/?f=p%28%5Ctext%7BA%20and%20B%20and%20C%7D%29%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%5Cfrac%7B1%7D%7B2%7D%5Ctimes%5Cfrac%7B1%7D%7B3%7D)
Hence the probability that box contain chocolate, chis and juice is ![\frac{1}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B24%7D)