July 5, 2018 MATH 3352 FINAL EXAM Page 3 a potnus) A type C battery is in workin

Question

July 5, 2018 MATH 3352 FINAL EXAM Page 3 a potnus) A type C battery is in working condition with probability 0.75, wherens a tyrpe battery is in working condition with probability 0.6. A battery is randomly chosen from a bin consisting of 4 type C, and 6 type D batteries. (a) (4 points) What is the probability that the battery does NOT wor Answer: (b) (4 points) Given that the battery does not work, what is the conditional probability that it was a type C battery? Answer: 18 3 of these bets. On each bet, she will either win $5 with probability 38 or lose $5 with probability3 (a) (4 points) What is the probability that she will place a total of 8 bets before she stops? 4. (8 points) A casino patron will coutinue to make $5 bets on red in roulette until she has won 20 Answer: (b) (4 points) What is her expected winnings when she stops? Answer:

Explanation / Answer

Question 3:

P( working | C ) = 0.75, P( working | D ) = 0.6

P(C) = 4/10 = 0.4 and P(D) = 6/10 = 0.6

Therefore using law of total probability, we get:

P( does not work ) = P( does not work | C)P(C) + P( does not work | D)P(D)

P( does not work ) = 0.25*0.4 + 0.4*0.6 = 0.1 + 0.24 = 0.34

Therefore 0.34 is the required probability here.

b) Given that the battery does not work, probability that it is C is computed using Bayes theorem as:

P( C | does not work ) = P( does not work | C)P(C) / P( does not work )

P( C | does not work ) = 0.25*0.4 / 0.34 = 0.2941

Therefore 0.2941 is the required probability here.

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

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