Question

aaron plays on a baseball team, and the probability that the team wins their next game is 0.25. aarons sister betty is on a basketball team. the probability that bettys team wins their next game is 0.36. the probability that both teams win their next game is 0.09. let a be the event that aarons team wins its next game, and let b be the event that bettys team wins its next game. select and move words into the spaces to correctly complete the sentence. dependent independent equal not equal product sum the events that aarons team and bettys team win their next games are ____, because p(a and b) is __ to the ____ of p(a) and p(b).

Explanation:

Step1: Recall the rule for independent events

For two events \(A\) and \(B\), if they are independent, \(P(A\cap B)=P(A)\times P(B)\).

Step2: Calculate \(P(A)\times P(B)\)

Given \(P(A) = 0.25\) and \(P(B)=0.36\), then \(P(A)\times P(B)=0.25\times0.36 = 0.09\).

Step3: Compare with \(P(A\cap B)\)

Since \(P(A\cap B) = 0.09\) and \(P(A)\times P(B)=0.09\), the two - values are equal.

Answer:

independent, equal, product