Question

a package contains 4 red, 2 green, 8 purple, and 6 blue jelly beans. what is the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean?

Explanation:

Step1: Calculate total number of jelly beans

Total number of jelly beans \(=4 + 2+8 + 6=20\)

Step2: Calculate probability of choosing purple jelly bean

Probability of choosing purple jelly bean \(P(\text{purple})=\frac{8}{20}=\frac{2}{5}\)
After eating the purple jelly bean, number of jelly beans left \(=20 - 1=19\)

Step3: Calculate probability of choosing blue jelly bean

Probability of choosing blue jelly bean \(P(\text{blue})=\frac{6}{19}\)

Step4: Calculate combined probability

Since these are two - step dependent events, use the formula \(P(A\text{ and }B)=P(A)\times P(B|A)\)
\(P(\text{purple then blue})=\frac{8}{20}\times\frac{6}{19}=\frac{48}{380}=\frac{12}{95}\)

Answer:

\(\frac{12}{95}\)