Questions: 6. 300 Women and 429 Men were asked about their choice of candy. What is the conditional probability with percentages if 69 women prefer skittles?. Show your work.
7. Conditional Probability with Bayes's Theorem:
P(A B) = (P(B A) * P(A)) / P(B)
Solve question 6 using Bayes's Theorem. Show your work.
Transcript text: 6. 300 Women and 429 Men were asked about their choice of candy. What is the conditional probability with percentages if 69 women prefer skittles?. Show your work.
7. Conditional Probability with Bayes's Theorem:
\[
P(A \mid B)=\frac{P(B \mid A) \times P(A)}{P(B)}
\]
Solve question 6 using Bayes's Theorem. Show your work.
Solution
Solution Steps
Step 1: Calculate P(Woman)
The probability that a randomly selected person is a woman is given by:
P(Woman)=300+429300=0.4115
Step 2: Calculate P(Skittles∣Woman)
The probability that a woman prefers Skittles is:
P(Skittles∣Woman)=30069=0.2300
Step 3: Calculate P(Skittles)
The overall probability that a randomly selected person prefers Skittles is:
P(Skittles)=300+42969=0.0947
Step 4: Apply Bayes's Theorem to find P(Woman∣Skittles)
Using Bayes's Theorem, we can find the probability that a person who prefers Skittles is a woman: