19. You are given: The probability that Tim will take a math class during the ne

Question

19. You are given: The probability that Tim will take a math class during the next year is one half of the probability that he will take a physics class next year. The probability that Tim will take a math class and a physics class next year is 200% of the product of the probability that he will take a math class next year and the probability that he will take a physics class next year. The probability that Tim will take either a math class or a physics class next year is 0.36. Calculate the probability that Tim will take a math class next year and he will not take a Physics class next year.

Explanation / Answer

19.

Let A be the event that he takes Math class

Let B be the event that he takes Physics class

P(time will take a Math class) = 1/2 * P( he takes physics ), P(A) = .5*P(B)

P( math class and physics) = 2*P( math class)*P(physcis class), P(A and B) = 2P(A)*P(B)

P( math or physics) = .36, P( A or B) = .36

P(A or B) = P(A)+P(B) - P(A and B)

.36 = .5P(B) + P(B) - 2*P(A)*P(B)

> .36 = .5P(B) + P(B) - 2*.5P(B)*P(B)

.36 = 1.5P(B) -P(B)^2

P(B)^2 - 1.5P(B) +.36 = 0, P(B) = 3/10 or 6/5

Probability cannot be more than 1, so P(B) = 3/10 = .3

So, P(A) = .5P(B) = .5*.3 = .15

P(A and B') = P( A only) = P(A) - P(A and B) = .15 - 2*.15*.30 = .06

So, Probability that Tim will take a math class next year but not a Physics class is .06

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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