Question

1. seth has 4 plaid shirts and 5 solid - colored shirts hanging together in a closet. in his haste to get ready for work, he randomly grabs 1 of these 9 shirts. what is the probability that the shirt seth grabs is plaid?

a. $\frac{1}{5}$
b. $\frac{1}{4}$
c. $\frac{4}{9}$
d. $\frac{1}{9}$
e. $\frac{4}{5}$

1. the daily totals of enrollment at sunnyside summer camp last monday through saturday were 17, 19, 23, 14, 25, and 28. what was the average number of enrollments per day?

a. 126
b. 28
c. 21
d. 18
e. 14

Explanation:

Question 3

Step1: Determine the probability formula

The probability \(P\) of an event is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

Step2: Identify the number of favorable and total outcomes

The number of favorable outcomes (plaid shirts) is \(n = 4\). The total number of outcomes (total shirts) is \(N=9\).

Step3: Calculate the probability

Using the formula \(P=\frac{n}{N}\), we substitute \(n = 4\) and \(N = 9\), so \(P=\frac{4}{9}\).

Step1: Recall the average formula

The average (mean) \(\bar{x}\) of a set of numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\).

Step2: Calculate the sum of the enrollments

\(\sum_{i=1}^{6}x_i=17 + 19+23+14+25+28=(17+19)+(23+14)+(25+28)=36+37+53 = 126\).

Step3: Calculate the average

Since \(n = 6\), using the formula \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), we substitute \(\sum_{i=1}^{6}x_i = 126\) and \(n = 6\), so \(\bar{x}=\frac{126}{6}=21\).

Answer:

C. \(\frac{4}{9}\)

Question 4