Suppose 16%of the population are 63 or over, 28% of those 63 or over have loans, and 54% of those under 63 have loans. Find the probabilities that a person fits into the following categories. (a) 63 or over and has a loan (b) Has a loan (c) Are the events that a person is 63 or over and that the person has a loan independent? Explain. Part 1 (a) The probability that a person is 63or over and has a loan is__ (Type an integer or decimal rounded to three decimal places as needed.) Part 2 (b) The probability that a person has a loan is. (Type an integer or decimal rounded to three decimal places as needed.) Part 3 (c) Let B be the event that a person is 63 or over. Let A be the event that a person has a loan. Are the events B and A independent? Select the correct choice below and fill in the answer box to complete your choice. A. Events B and A are independent if and only if P(B ∪ A)=P(B)+P(A). The value of P(B) is, Since P(B ∪ A)≠P(B)+P(A), events B and A are not independent. B. Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A).The value of P(B) is, Since P(B ∩ A)=P(B)•P(A), events B and A are independent. C. Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A). The value of P(B) is_, Since P(B ∩ A)≠P(B)•P(A), events B and A are not independent. D. Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A|B).The value of P(B) is_ and the value of P(A|B) is__. Since P(B ∩ A)=P(B)•P(A|B), events B and A are independent.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.2: Introduction To Probability

Problem 105E: Refugees In a refugee camp in southern Mexico it was found that 90 of the refugees came to escape...

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Part 1 (a) The probability that a person is 63or over and has a loan is____ (Type an integer or decimal rounded to three decimal places as needed.)

Part 2 (b) The probability that a person has a loan is____. (Type an integer or decimal rounded to three decimal places as needed.)

Part 3 (c) Let B be the event that a person is 63 or over. Let A be the event that a person has a loan. Are the events B and A independent? Select the correct choice below and fill in the answer box to complete your choice.

A. Events B and A are independent if and only if P(B ∪ A)=P(B)+P(A). The value of P(B) is__, Since P(B ∪ A)≠P(B)+P(A), events B and A are not independent.

Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A).The value of P(B) is__, Since P(B ∩ A)=P(B)•P(A), events B and A are independent.

C. Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A). The value of P(B) is___, Since P(B ∩ A)≠P(B)•P(A), events B and A are not independent.

Events B and A are independent if and only if P(B ∩ A)=P(B)•P(A|B).The value of P(B) is___ and the value of P(A|B) is____. Since P(B ∩ A)=P(B)•P(A|B),
events B and A are independent.

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Part 1 ​(a​) The probability that a person is 63or over and has a loan is____ ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Part 2 ​(b) The probability that a person has a loan is____. ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Part 3 ​(c) Let B be the event that a person is 63 or over. Let A be the event that a person has a loan. Are the events B and A​ independent? Select the correct choice below and fill in the answer box to complete your choice.

Part 1 (a) The probability that a person is 63or over and has a loan is____ (Type an integer or decimal rounded to three decimal places as needed.)

Part 2 (b) The probability that a person has a loan is____. (Type an integer or decimal rounded to three decimal places as needed.)

Part 3 (c) Let B be the event that a person is 63 or over. Let A be the event that a person has a loan. Are the events B and A independent? Select the correct choice below and fill in the answer box to complete your choice.