Boba Fett, The Famous Bounty Hunter, Uses Various Methods ✓ Solved

Boba Fett, the famous bounty hunter use a variety of methods

Boba Fett, the famous bounty hunter, uses a variety of methods to detain the criminals he apprehends. In the past, he is known to have used a blaster rifle, carbonite, and a stun gun. The probabilities associated with him using each of these three methods are shown in the table below. What is the probability of selecting three of the criminals he has apprehended and find out that he froze all three of them using carbonite?

Carbonite 4.5% Blaster Rifle 89.5% Stun Gun 6.0%

QUESTION 1: ObeWan, Inc. manufactures light sabers in their plant on Naboo. Quality inspectors want to determine if the products meet their standards, so they inspect a batch of 30 light sabers, three of which are defective. If two light sabers are drawn randomly, one at a time without replacement, what is the probability that both are defective?

QUESTION 2: ObeWan, Inc. manufactures light sabers in their plant on Naboo. Quality inspectors want to determine if the products meet their standards, so they inspect a batch of 30 light sabers, five of which are defective. If three light sabers are drawn randomly, one at a time with replacement, what is the probability that all 3 are defective?

QUESTION 3: You are putting together a trip to Kamino to pick up some clones and need to take some droids along to perform various functions. You have 10 droids from which to select. You decide that you can make do if you take 3 of the droids with you. Based on this, how many different groups of droids could you possibly take with you to Kamino?

QUESTION 4: Princess Leia and Han Solo are planning their wedding. In order to decorate, they have gotten some potted plants to decorate the reception hall. They want to determine how many different ways they can arrange the following plants: 8 Black Lily, 5 Anagallis, and 4 Zinthorns.

QUESTION 5: The police in Tipoca City have collected data over a period of 300 days for fatal accidents involving cloud cars. The data is presented below. How many accidents can the police expect, on average?

QUESTION 6: Watoo sells fan blades for pod racers in batches of 1,000 units only. The daily demand for these fan blades and the respective probabilities are given below. What is Watoo's expected daily demand in units for these fan blades?

QUESTION 7: Watoo sells replacement fan blades for pod racers. The daily sales for these fan blades and the respective probabilities are given below. Assume that Watoo sells these fan blades for $4.50 per unit. What is his expected daily revenue if demand is met?

QUESTION 8: A group of researchers is investigating jungles of Kashyyk in search of Wookies. There is a 35% probability that they will actually see a Wookie in the village among the giant wroshyr trees. However, the probability that they will see a Bantha during their expedition is 47 percent. 30% of the time, the researchers will see neither a Wookie nor a Bantha. If a researcher is selected at random, what is the probability that the researcher saw a Wookie? If a researcher is selected at random, what is the probability that the researcher saw a Bantha? If a researcher is selected at random, what is the probability that the researcher saw neither a Wookie or a Bantha? If a researcher is selected at random, what is the probability that the researcher saw both a Wookie and Bantha?

QUESTION 9: Given that a researcher saw a Wookie, what is the probability that the researcher saw a Bantha? Given that a researcher did not see a Bantha, what is the probability that the researcher saw a Wookie?

QUESTION 10: In order to crush the rebels, it is necessary to have a constant flow of Storm Troopers arriving at the Death Star. It is assumed that the arrival of Imperial Storm Troopers follows a Poisson distribution. If they arrive at the Death Star at a rate of 3 per hour, what is the probability that: (1) Exactly 7 will arrive in the next hour? (2) Fewer than 5 will arrive in the next hour? (3) More than 4 will arrive in the next hour? (4) Exactly 3 will arrive in the next 2 hours? (5) Fewer than 8 will arrive in the next 30 minutes?

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The analysis of probabilities plays a pivotal role in fields such as statistics, engineering, science, and even decision-making in everyday situations. In particular, the examination of Boba Fett’s methods of apprehending criminals through probabilities offers insights not only into fictional character actions but also into real-world applications of probability theory.

The probability of Boba Fett successfully freezing three criminals using carbonite can be calculated using the formula for independent events. Given that the probability of him using carbonite is 4.5%, the probability that he freezes all three criminals can be calculated by multiplying the individual probabilities:

P(All three using carbonite) = P(Carbonite) × P(Carbonite) × P(Carbonite) = (0.045) × (0.045) × (0.045) = 0.000097175.

This answers the first question, indicating that there is a 0.0097175% chance of this happening.

Next, we examine the light sabers manufactured by ObeWan, Inc. For QUESTION 1, we need to find the probability that both drawn light sabers, selected one at a time, are defective. There are three defective light sabers in the batch of 30. The probability of drawing the first defective light saber is:

P(First defective) = 3/30 = 0.1. The total now becomes 29 light sabers, with 2 defective remaining:

P(Second defective | First defective) = 2/29 = 0.069.

The total probability becomes:

P(Both defective) = P(First defective) P(Second defective) = (3/30) (2/29) = 0.1 * 0.069 = 0.0069 or approximately 0.69%.

For QUESTION 2, with five defective light sabers and three drawn with replacement, the probability of selecting three defective light sabers is the product of probabilities for each selection:

P(All defective with replacement) = (5/30) × (5/30) × (5/30) = (1/6) × (1/6) × (1/6) = 0.0123.

QUESTION 3 presents a combination problem where the number of ways to choose 3 droids from 10 can be calculated using the combination formula:

C(n, k) = n! / (k!(n-k)!), thus C(10, 3) = 10! / (3!7!) = 120.

For QUESTION 4, the arrangements of plants can be calculated by using the formula for permutations of multiset:

P = n!/n1! n2! n3! = 17!/(8!5!4!), which simplifies to equal 25740.

In QUESTION 5, the police can expect an average number of fatal accidents using data over 300 days, averaging results to gain insight on trends.

In terms of demand and revenue calculations, for QUESTION 6 about Watoo’s fan blades, the expected daily demand can be calculated using the probabilities given.

Moreover, for QUESTION 8 presenting insights into the probabilities of seeing Wookies and Banthas, conditional probabilities and the construction of probability matrices can help derive these figures accurately.

Across all these questions, probability calculations allow for the understanding of complex decision-making processes, assisting industries and decisions grounded in data-based analyses.

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