Questions: Select the correct answer from the drop-down menu. The probability that Jane will go to a ballgame (event A) on a Monday is 0.73, and the probability that Kate will go to a ballgame (event B) the same day is 0.61. The probability that Kate and Jane both go to the ballgame on Monday is 0.52. From the given scenario, we can conclude that events A and B are.

Solution Steps

To determine if events \( A \) and \( B \) are independent, we first calculate the product of their individual probabilities:

\[ P(A) = 0.73, \quad P(B) = 0.61 \]

The product of these probabilities is:

\[ P(A) \times P(B) = 0.73 \times 0.61 = 0.4453 \]

Next, we compare the product \( P(A) \times P(B) \) with the given probability of both events occurring, \( P(A \cap B) \):

\[ P(A \cap B) = 0.52 \]

For events \( A \) and \( B \) to be independent, the following condition must hold:

\[ P(A \cap B) = P(A) \times P(B) \]

Substituting the values, we have:

\[ 0.52 \neq 0.4453 \]

Since \( P(A \cap B) \neq P(A) \times P(B) \), events \( A \) and \( B \) are not independent.

Final Answer