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

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|\np(coffee|small) = \\frac{7}{20}\nenter as a decimal rounded to the nearest hundredth.\np(coffee|small) = ?

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|\np(coffee|small) = \\frac{7}{20}\nenter as a decimal rounded to the nearest hundredth.\np(coffee|small) = ?

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the table, $P(\text{coffee}|\text{small})=\frac{\text{Number of small coffees}}{\text{Total number of small drinks}}$.

Step2: Identify values from the table

The number of small coffees is 7 and the total number of small drinks is 20. So $P(\text{coffee}|\text{small})=\frac{7}{20}$.

Step3: Convert to decimal

To convert $\frac{7}{20}$ to a decimal, we divide 7 by 20: $7\div20 = 0.35$.

Answer:

$0.35$