A taste test for a new coffee brand was performed, with results recorded in the

Question

A taste test for a new coffee brand was performed, with results recorded in the probability model at right. All four table probabilities sum to 100%, but two of these probabilities (shown here as x and y) were accidentally lost. Enjoyed taste? Yes. No Male. X. 18.4% Female 32%. Y
Let A - “did enjoy the taste” Let B- “is female” Using this given table:
A) find P(A). Also, find P(B). [these answers will include numbers along with symbols x and y] B) find P( A and B). [Hint: Find this single probability value by direct-inspection of the tables.] C) write an equation showing these four table values added together, and equaling their required sum. D) if event A is independent of event B, then the product of your answers in part (a) must equal your answer in part (b). Can we find percentage value for x and y that solve this equation? If so, find all such solutions. If not, say why not. [Hint: try using part (c), to make a variable substitution.] A taste test for a new coffee brand was performed, with results recorded in the probability model at right. All four table probabilities sum to 100%, but two of these probabilities (shown here as x and y) were accidentally lost. Enjoyed taste? Yes. No Male. X. 18.4% Female 32%. Y
Let A - “did enjoy the taste” Let B- “is female” Using this given table:
A) find P(A). Also, find P(B). [these answers will include numbers along with symbols x and y] B) find P( A and B). [Hint: Find this single probability value by direct-inspection of the tables.] C) write an equation showing these four table values added together, and equaling their required sum. D) if event A is independent of event B, then the product of your answers in part (a) must equal your answer in part (b). Can we find percentage value for x and y that solve this equation? If so, find all such solutions. If not, say why not. [Hint: try using part (c), to make a variable substitution.] Enjoyed taste? Yes. No Male. X. 18.4% Female 32%. Y
Let A - “did enjoy the taste” Let B- “is female” Using this given table:
A) find P(A). Also, find P(B). [these answers will include numbers along with symbols x and y] B) find P( A and B). [Hint: Find this single probability value by direct-inspection of the tables.] C) write an equation showing these four table values added together, and equaling their required sum. D) if event A is independent of event B, then the product of your answers in part (a) must equal your answer in part (b). Can we find percentage value for x and y that solve this equation? If so, find all such solutions. If not, say why not. [Hint: try using part (c), to make a variable substitution.]

Explanation / Answer

A )

P(A) = 18.4% + Y

P(B) = 32% + Y

B )

P(A and B ) = Y

C )

X+Y+ 32% + 18.4 % = 100 %

D )

Independent events, so P( A and B ) = P(A)*P(B)

Y= (18.4% + Y)*(32% + Y) --------------- Equation 1

Solve for Y you get Y = 20.08 %

Using equation that you got in C , X+Y= 49.6 %

you get X = 29.52 %

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.