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 large, given that they ordered a hot drink.\np(large | hot) = \\frac{p(large and hot)}{p(hot)} = ?

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 large, given that they ordered a hot drink.\np(large | hot) = \\frac{p(large and hot)}{p(hot)} = ?

Answer

Explanation:

Step1: Identify values from table

The number of customers who ordered a large and hot drink is 22, so $P(\text{large and hot})=\frac{22}{100}$. The number of customers who ordered a hot drink is 75, so $P(\text{hot})=\frac{75}{100}$.

Step2: Calculate conditional - probability

Using the formula $P(\text{large}|\text{hot})=\frac{P(\text{large and hot})}{P(\text{hot})}$, we substitute the values: $P(\text{large}|\text{hot})=\frac{\frac{22}{100}}{\frac{75}{100}}=\frac{22}{75}\approx0.29$.

Answer:

$0.29$