Statistical Thinking September 24, 2018 1. A bin contains 3 different types of d

Question

Statistical Thinking September 24, 2018 1. A bin contains 3 different types of disposable flashlights. The probability that a type 1 flashlight will give over 100 hours of use is 0.7, with the corresponding probabilities for type 2 and type 3 flashlights being 0.4 and 0.3 respectively. Suppose that 20% of the flashlights in MATH 216 Bayes's rule practice problems the bin are type 1, 30% are type 2 and 50% are type 3. (a) What is the probability that a randomly chosen flashlight will give more than 100 hours of use? (b) Given the flashlight lasted over 100 hours, what is the probability that it was type 3 flashlight?

Explanation / Answer

Answer:

given data:

here we need to find out the :

A.what is the probability that randomly chosen flash light will given more then 100 hours of use?

(P(Type1) = 20/100 = 0.2, P(Type2) = 30/100 = 0.3, P(Type4) = 50/100 = 0.5

P(Type 1 and >100 hours) = 0.2 * 0.7 = 0.14

P(Type 2 and > 100 hours) = 0.3 * 0.4 = 0.12

P(Type 3 and >100 hours) = 0.5 * 0.3 = 0.15

Therefore the probability of a flashlight which is picked will give more than 100 hours = 0.14+0.12+0.15 = 0.51

B.given the flash light lasted over 100 hours, what is the probability that it was type 3 flash light?

(b) Given it last > 500 hours, probability it is a Type 1 flashlight

P(Type 1/Lasts > 100hrs) = P(Type 1 and lasts >100 hours)/P(lasts>100 hours) = 0.14/0.51 = 0.2745

P(Type 2/Lasts > 100hrs) = P(Type 2 and lasts >100 hours)/P(lasts>100 hours) = 0.12/0.51 = 0.2353

P(Type 3/Lasts > 100hrs) = P(Type 3 and lasts >100 hours)/P(lasts>100 hours) = 0.15/0.51 = 0.2941

(PN: in part b, all the values are taken from part (a))

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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