For the following unrelated parts consider the following scenario. Nathan inadve

Question

For the following unrelated parts consider the following scenario. Nathan inadvertently mixed up six new batteries and four dead batteries in a drawer. When you are asked to find a probability calculate it to four decimal places.
(a) If Nathan randomly selects one battery from the ten batteries, what is the probability that it is a dead battery?
(b) If the ten batteries are all distinguishable, in how many different ways can Nathan put two batteries in a flashlight, four batteries in a radio, and four batteries in a camera?
(c) If Nathan randomly selects four batteries from the ten batteries to install in a radio and the radio works only if none of the batteries is dead, what is the probability that the radio works?
(d) If Nathan randomly selects a battery from the ten batteries and puts it in a toy pink bunny, and then randomly selects another battery from the remaining batteries and puts it in a second toy pink bunny, what is the probability that both bunnies operate? What is the probability that only one bunny operates? What is the probability that neither bunny operates?
(e) Nathan randomly selects a battery from the ten batteries for his MP3 player, but is interrupted by a phone call. While he is answering the call his wife returns the battery to the drawer. After hanging up Nathan again selects a battery for his MP3 player. What is the probability that at least one of his two selections results in a dead battery?
For the following unrelated parts consider the following scenario. Nathan inadvertently mixed up six new batteries and four dead batteries in a drawer. When you are asked to find a probability calculate it to four decimal places.
(a) If Nathan randomly selects one battery from the ten batteries, what is the probability that it is a dead battery?
(b) If the ten batteries are all distinguishable, in how many different ways can Nathan put two batteries in a flashlight, four batteries in a radio, and four batteries in a camera?
(c) If Nathan randomly selects four batteries from the ten batteries to install in a radio and the radio works only if none of the batteries is dead, what is the probability that the radio works?
(d) If Nathan randomly selects a battery from the ten batteries and puts it in a toy pink bunny, and then randomly selects another battery from the remaining batteries and puts it in a second toy pink bunny, what is the probability that both bunnies operate? What is the probability that only one bunny operates? What is the probability that neither bunny operates?
(e) Nathan randomly selects a battery from the ten batteries for his MP3 player, but is interrupted by a phone call. While he is answering the call his wife returns the battery to the drawer. After hanging up Nathan again selects a battery for his MP3 player. What is the probability that at least one of his two selections results in a dead battery?
For the following unrelated parts consider the following scenario. Nathan inadvertently mixed up six new batteries and four dead batteries in a drawer. When you are asked to find a probability calculate it to four decimal places.
(a) If Nathan randomly selects one battery from the ten batteries, what is the probability that it is a dead battery?
(b) If the ten batteries are all distinguishable, in how many different ways can Nathan put two batteries in a flashlight, four batteries in a radio, and four batteries in a camera?
(c) If Nathan randomly selects four batteries from the ten batteries to install in a radio and the radio works only if none of the batteries is dead, what is the probability that the radio works?
(d) If Nathan randomly selects a battery from the ten batteries and puts it in a toy pink bunny, and then randomly selects another battery from the remaining batteries and puts it in a second toy pink bunny, what is the probability that both bunnies operate? What is the probability that only one bunny operates? What is the probability that neither bunny operates?
(e) Nathan randomly selects a battery from the ten batteries for his MP3 player, but is interrupted by a phone call. While he is answering the call his wife returns the battery to the drawer. After hanging up Nathan again selects a battery for his MP3 player. What is the probability that at least one of his two selections results in a dead battery?
For the following unrelated parts consider the following scenario. Nathan inadvertently mixed up six new batteries and four dead batteries in a drawer. When you are asked to find a probability calculate it to four decimal places.
(a) If Nathan randomly selects one battery from the ten batteries, what is the probability that it is a dead battery?
(b) If the ten batteries are all distinguishable, in how many different ways can Nathan put two batteries in a flashlight, four batteries in a radio, and four batteries in a camera?
(c) If Nathan randomly selects four batteries from the ten batteries to install in a radio and the radio works only if none of the batteries is dead, what is the probability that the radio works?
(d) If Nathan randomly selects a battery from the ten batteries and puts it in a toy pink bunny, and then randomly selects another battery from the remaining batteries and puts it in a second toy pink bunny, what is the probability that both bunnies operate? What is the probability that only one bunny operates? What is the probability that neither bunny operates?
(e) Nathan randomly selects a battery from the ten batteries for his MP3 player, but is interrupted by a phone call. While he is answering the call his wife returns the battery to the drawer. After hanging up Nathan again selects a battery for his MP3 player. What is the probability that at least one of his two selections results in a dead battery?

Explanation / Answer

For the following unrelated parts consider the following scenario. Nathan inadvertently mixed up six new batteries and four dead batteries in a drawer.

(a) If Nathan randomly selects one battery from the ten batteries, what is the probability that it is a dead battery?

Answer: Pr(Dead battery if one selcted) = 4/10 = 0.4000

(b) If the ten batteries are all distinguishable, in how many different ways can Nathan put two batteries in a flashlight, four batteries in a radio, and four batteries in a camera?

Answer: Number of ways he can put 10 batteries in the given way is = 10C2 * 8C4 * 4C4 = 3150

(c) If Nathan randomly selects four batteries from the ten batteries to install in a radio and the radio works only if none of the batteries is dead, what is the probability that the radio works?

Pr(All 4 batteries selcted are good batteries) = 6C4 * 4C0/10C4 = 360/ 5040 = 0.0714

(d) If Nathan randomly selects a battery from the ten batteries and puts it in a toy pink bunny, and then randomly selects another battery from the remaining batteries and puts it in a second toy pink bunny, what is the probability that both bunnies operate? What is the probability that only one bunny operates? What is the probability that neither bunny operates?

Answer : Pr(Both bunny operate) = Pr(First bunny operate) * Pr(second bunny operate) = (6/10) * (5/9) = 1/3

Pr(One of bunny operate) = Pr(first bunny operate) * Pr(second bunny dont operate) + Pr(first bunny doesn't operate) * Pr(second bunny operate) = 6/10 * 4/9 + 4/10 * 6/9 = 8/15

Pr(No bunny operate) = Pr(first bunny fail) * Pr(second bunny fail) = 4/10 * 3/9 = 2/15

(e) Nathan randomly selects a battery from the ten batteries for his MP3 player, but is interrupted by a phone call. While he is answering the call his wife returns the battery to the drawer. After hanging up Nathan again selects a battery for his MP3 player. What is the probability that at least one of his two selections results in a dead battery?

Pr(at least one of his two selection results in dead battery) = 1 - Pr(both selection results in good battery)

Pr(both selection results in good battery) = Pr(first picked battery out of 10 is good) * Pr(Second icked battery out of 10 is good)

= 6/10 * 6/10 = 0.36

Pr(at least one of his two selection results in dead battery) = 1 - Pr(both selection results in good battery)  

= 1 - 0.36 = 0.64

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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