Question

1. gift baskets the gift basket store had the following premade gift baskets containing the following combina - tions in stock. choose 1 basket at random. find the probability that it contains a. coffee or candy b. tea given that it contains mugs c. tea and cookies source: www.infoplease.com

Explanation:

Step1: Calculate total number of baskets

Sum all the values in the table: \(20 + 13+10 + 12+10 + 12=\sum_{i = 1}^{6}x_{i}=77\)

Step2: Calculate for part a (Coffee or candy)

Number of coffee baskets: \(20 + 13+10=43\)
Number of candy baskets: \(10 + 12=22\)
Number of baskets that are both coffee and candy: \(10\)
Using the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(P(\text{Coffee}\cup\text{Candy})=\frac{43 + 22- 10}{77}=\frac{55}{77}=\frac{5}{7}\)

Step3: Calculate for part b (Tea given that it contains mugs)

Number of baskets with mugs: \(13 + 10=23\)
Number of baskets with tea and mugs: \(10\)
Using the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\)
\(P(\text{Tea}|\text{Mugs})=\frac{10}{23}\)

Step4: Calculate for part c (Tea and cookies)

Number of baskets with tea and cookies: \(12\)
\(P(\text{Tea}\cap\text{Cookies})=\frac{12}{77}\)

Answer:

a. \(\frac{5}{7}\)
b. \(\frac{10}{23}\)
c. \(\frac{12}{77}\)