find the probability that a drink is a coffee, given it is a small.\n| | large | small | total…

find the probability that a drink is a coffee, given it is a small.\n| | large | small | total |\n|--|--|--|--|\n| coffee | 8 | 7 | 15 |\n| tea | 5 | 13 | 18 |\n| total | 13 | 20 | 33 |\nfirst, find the probability of a drink being a small coffee.\np(coffee | small) = \\frac{p(small and coffee)}{p(small)}\np(small and coffee) = \\frac{?}{33}

find the probability that a drink is a coffee, given it is a small.\n| | large | small | total |\n|--|--|--|--|\n| coffee | 8 | 7 | 15 |\n| tea | 5 | 13 | 18 |\n| total | 13 | 20 | 33 |\nfirst, find the probability of a drink being a small coffee.\np(coffee | small) = \\frac{p(small and coffee)}{p(small)}\np(small and coffee) = \\frac{?}{33}

Answer

Explanation:

Step1: Identify number of small - coffees

The number of small - coffees is 7.

Step2: Calculate probability of small and coffee

The total number of drinks is 33. The probability of a drink being a small and coffee is the number of small - coffees divided by the total number of drinks. So $P(\text{small and coffee})=\frac{7}{33}$.

Step3: Calculate probability of coffee given small

We know that $P(\text{coffee}|\text{small})=\frac{P(\text{small and coffee})}{P(\text{small})}$. The number of small drinks is 20, so $P(\text{small})=\frac{20}{33}$. Then $P(\text{coffee}|\text{small})=\frac{\frac{7}{33}}{\frac{20}{33}}=\frac{7}{20}=0.35$.

Answer:

$0.35$