A bin contains 3 different types of disposable flashlights. The probability that

Question

A bin contains 3 different types of disposable flashlights. The probability that a type 1 flashlight will give over 100 hours of use is .7, with the corresponding probabilities for types 2 and 3 being .4 and .3 respectively. Suppose that 20 percent of the flashlights in the bin are type 1, 30 percent of type 2, and 50 percent of type 3. What is the probability that a randomly chosen flashlight will give more than 100 hours of use? Given the flashlight lasted over 100 hours, what is the probability that it was a type j flashlight, j = 1, 2, 3.

Explanation / Answer

(a) 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 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 A
• Subjects

---

---

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