Question

the probability that peggy has math homework is 0.35. the probability that peggy has english homework is 0.40. the probability that peggy has homework in both classes is 0.14. let a be the event that peggy has math homework and let b be the event that peggy has english homework. move words into the spaces to complete the sentence. the events of peggy having math homework and english homework are ____ because p(a and b) is __ to the ____ of p(a) and p(b). dependent independent equal not equal product sum

Explanation:

Step1: Recall the condition for independent events

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

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

Given \(P(A) = 0.35\) and \(P(B)=0.40\), then \(P(A)\times P(B)=0.35\times0.40 = 0.14\).

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

We know \(P(A\cap B) = 0.14\), since \(P(A\cap B)=P(A)\times P(B)\), the events are independent.

Answer:

independent, equal, product