the probability that peggy has math homework is 0.35. the probability that peggy has english homework is…
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 equal product independent not equal sum
Answer
Explanation:
Step1: Recall independence - condition
For two events (A) and (B) to be independent, (P(A\cap B)=P(A)\times P(B)). Calculate (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). And (P(A\cap B)=0.14).
Step3: Determine independence
Since (P(A\cap B)=P(A)\times P(B)), the events are independent.
Answer:
The events of Peggy having math homework and English homework are independent because (P(A) and (B)) is equal to the product of (P(A)) and (P(B)).