at a coffee shop, the first 100 customers orders were as follows.\n| | small | medium | large | total…

at a coffee shop, the first 100 customers orders were as follows.\n| | small | medium | large | total |\n|--|--|--|--|--|\n| hot | 5 | 48 | 22 | 75 |\n| cold | 8 | 12 | 5 | 25 |\n| total | 13 | 60 | 27 | 100 |\nfind the probability a customer ordered a medium, given that they ordered a cold drink.\np(medium | cold) = \\frac{p(medium and cold)}{p(cold)} = ?\nround to the nearest hundredth.

at a coffee shop, the first 100 customers orders were as follows.\n| | small | medium | large | total |\n|--|--|--|--|--|\n| hot | 5 | 48 | 22 | 75 |\n| cold | 8 | 12 | 5 | 25 |\n| total | 13 | 60 | 27 | 100 |\nfind the probability a customer ordered a medium, given that they ordered a cold drink.\np(medium | cold) = \\frac{p(medium and cold)}{p(cold)} = ?\nround to the nearest hundredth.

Answer

Explanation:

Step1: Identify P(medium and cold)

From the table, the number of customers who ordered a medium - cold drink is 12. So, $P(\text{medium and cold})=\frac{12}{100}$.

Step2: Identify P(cold)

From the table, the number of customers who ordered a cold drink is 25. So, $P(\text{cold})=\frac{25}{100}$.

Step3: Calculate P(medium|cold)

Using the formula $P(\text{medium}|\text{cold})=\frac{P(\text{medium and cold})}{P(\text{cold})}$, we substitute the values: $P(\text{medium}|\text{cold})=\frac{\frac{12}{100}}{\frac{25}{100}}=\frac{12}{25}= 0.48$.

Answer:

0.48