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.

Solution Steps

The probability that a randomly selected person is a woman is given by:

\[ P(\text{Woman}) = \frac{300}{300 + 429} = 0.4115 \]

The probability that a woman prefers Skittles is:

\[ P(\text{Skittles} \mid \text{Woman}) = \frac{69}{300} = 0.2300 \]

The overall probability that a randomly selected person prefers Skittles is:

\[ P(\text{Skittles}) = \frac{69}{300 + 429} = 0.0947 \]

Using Bayes's Theorem, we can find the probability that a person who prefers Skittles is a woman:

\[ P(\text{Woman} \mid \text{Skittles}) = \frac{P(\text{Skittles} \mid \text{Woman}) \times P(\text{Woman})}{P(\text{Skittles})} \]

Substituting the values we calculated:

\[ P(\text{Woman} \mid \text{Skittles}) = \frac{0.2300 \times 0.4115}{0.0947} = 1.0000 \]

The probability \( P(\text{Woman} \mid \text{Skittles}) \) in percentage is:

\[ P(\text{Woman} \mid \text{Skittles}) \times 100 = 100.00\% \]

Final Answer