Question

ap stats lesson 5.3 homework
1 a variety pack (box) of instant oatmeal contains 30 packets of five different flavors of oatmeal. the number of packets of each variety is given in the table.

suppose that you randomly select a packet from a full box
a what is the probability that you select a plain oatmeal? use proper notation.
b. what is the probability that you dont select a plain oatmeal? use proper notation.
c what is the probability that you select a peach flavored oatmeal? use proper notation.
d. what is the probability that you select either cinnamon or brown sugar flavored oatmeal? use proper notation.

Explanation:

a. Probability of selecting plain oatmeal

Step1: Recall probability formula

Probability \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, number of plain oatmeal packets \(n(\text{Plain}) = 10\), total number of packets \(N=30\).

Step2: Calculate probability

\(P(\text{Plain})=\frac{10}{30}=\frac{1}{3}\approx 0.33\)

Step1: Use complement rule

The complement rule states \(P(\overline{A}) = 1 - P(A)\). We know \(P(\text{Plain})=\frac{1}{3}\) from part (a).

Step2: Calculate probability

\(P(\text{not Plain})=1 - P(\text{Plain})=1-\frac{1}{3}=\frac{2}{3}\approx 0.67\)

Step1: Find number of peach packets

First, find the number of peach packets. Let the number of peach packets be \(x\). Then \(10 + 5+8 + 4+x=30\). Solving for \(x\): \(x=30-(10 + 5+8 + 4)=3\)

Step2: Calculate probability

Using \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\), \(P(\text{Peach})=\frac{3}{30}=\frac{1}{10}=0.1\)

Answer:

\(P(\text{Plain})=\frac{1}{3}\approx 0.33\)

b. Probability of not selecting plain oatmeal