Question

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 . NextReset

Answer 1

Events A and B are called independent, when

$Pr(A\cap B)=Pr(A)\cdot Pr(B),$

otherwise events A and B are dependent.

The events A, B and A∩B are:

• A - Jane will go to a ballgame on Monday;
• B - Kate will go to a ballgame on Monday;
• A∩B - Kate and Jane both go to the ballgame on Monday.

$Pr(A)=0.73,\ Pr(B)=0.61,\ Pr(A\cap B)=0.52.\\ \\ Pr(A)\cdot Pr(B)=0.73\cdot 0.61=0.4453\neq 0.52=Pr(A\cap B).$

Answer: events A and B are dependent

Answer 2

From the given scenario, we can conclude that events A and B are dependent.

What are independent events?

Two events, A and B are independent, if:

$P(A \cap B) = P(A)P(B)$

In this problem, the events are:

• Event A: Jane goes to the ballgame.

• Event B: Kate goes to the ballgame.

For the probabilities, we have that:

$P(A) = 0.73, P(B) = 0.61, P(A \cap B) = 0.52$

The multiplication of the probabilities is:

$P(A)P(B) = 0.73(0.61) = 0.4453$

Since $P(A)P(B) \neq P(A \cap B)$, the events are not independent.

You can learn more about independent events at https://brainly.com/question/14478923