a package contains 4 red, 2 green, 8 purple, and 6 blue jelly beans. what is the probability of choosing a…

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?\n$\frac{1}{400}$\n$\frac{1}{380}$\n$\frac{3}{25}$\n$\frac{12}{95}$

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?\n$\frac{1}{400}$\n$\frac{1}{380}$\n$\frac{3}{25}$\n$\frac{12}{95}$

Answer

Explanation:

Step1: Calculate total number of jelly - beans

The total number of jelly - beans initially is $4 + 2+8 + 6=20$.

Step2: Calculate probability of choosing a purple jelly - bean first

The probability of choosing a purple jelly - bean on the first draw is $P(\text{purple})=\frac{8}{20}=\frac{2}{5}$, since there are 8 purple jelly - beans out of 20 total.

Step3: Calculate number of jelly - beans left after eating a purple one

After eating a purple jelly - bean, there are $20 - 1=19$ jelly - beans left.

Step4: Calculate probability of choosing a blue jelly - bean second

The probability of choosing a blue jelly - bean on the second draw, given that a purple jelly - bean was chosen first, is $P(\text{blue})=\frac{6}{19}$, since there are 6 blue jelly - beans out of the remaining 19.

Step5: Calculate the combined probability

By the multiplication rule for dependent events $P(A\cap B)=P(A)\times P(B|A)$, the probability of choosing a purple jelly - bean first and then a blue jelly - bean is $\frac{2}{5}\times\frac{6}{19}=\frac{12}{95}$.

Answer:

$\frac{12}{95}$