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 cold drink, given that they ordered a small.\np(cold | small) = \\frac{p(cold and small)}{p(small)} = ?\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 cold drink, given that they ordered a small.\np(cold | small) = \\frac{p(cold and small)}{p(small)} = ?\nround to the nearest hundredth.

Answer

Explanation:

Step1: Identify relevant values

$P(\text{cold and small})=\frac{8}{100}$, $P(\text{small})=\frac{13}{100}$

Step2: Calculate conditional probability

$P(\text{cold}|\text{small})=\frac{P(\text{cold and small})}{P(\text{small})}=\frac{\frac{8}{100}}{\frac{13}{100}}=\frac{8}{13}\approx 0.62$

Answer:

$0.62$