11. Your fortune teller's jar contains 50 cards. Each card is labeled with a predicted theme that will strongly influence how you experience the neNt year. The number of cards for each of the 4 themes is as follows: 10 "lucky", 20 "sad", 15 "powerful", and 5 "kind". Detemine the probability of drawing the following: (You can leave answers in fractional form) On a single draw, "lucky". On a single draw, "sad" or "powerful". Drawing a "sad" and then, after replacing it, a "lucky". Drawing a sequence of "lucky", "kind", and "kind" (without replacement). a. d.
11. Your fortune teller's jar contains 50 cards. Each card is labeled with a predicted theme that will strongly influence how you experience the neNt year. The number of cards for each of the 4 themes is as follows: 10 "lucky", 20 "sad", 15 "powerful", and 5 "kind". Detemine the probability of drawing the following: (You can leave answers in fractional form) On a single draw, "lucky". On a single draw, "sad" or "powerful". Drawing a "sad" and then, after replacing it, a "lucky". Drawing a sequence of "lucky", "kind", and "kind" (without replacement). a. d.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Step 2**
**b)**
**a)**
**Probability of drawing a lucky card on a single draw:**
\[ P = \frac{\text{Total number of lucky cards}}{\text{Total number of cards}} \]
\[ = \frac{10}{50} \]
\[ = \frac{1}{5} \]
**b)**
**Probability of drawing a sad or powerful card in a single draw:**
\[ P = \frac{\text{Total number of sad cards}}{\text{Total number of cards}} + \frac{\text{Total number of powerful cards}}{\text{Total number of cards}} \]
\[ = \frac{20}{50} + \frac{15}{50} \]
\[ = \frac{35}{50} \]
\[ = \frac{7}{10} \]
---
**Step 3**
**c)**
**c)**
\[ P = \left( \frac{\text{Total number of sad cards}}{\text{Total number of cards}} \right) \left( \frac{\text{Total number of lucky cards}}{\text{Total number of cards}} \right) \]
\[ = \frac{20}{50} \times \frac{10}{50} \]
\[ = \frac{2}{25} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dee35c8-07bc-4f6f-8047-1c0be93c606e%2F62093597-033a-47f2-b512-dc1d9143cb00%2F00onoaw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Step 2**
**b)**
**a)**
**Probability of drawing a lucky card on a single draw:**
\[ P = \frac{\text{Total number of lucky cards}}{\text{Total number of cards}} \]
\[ = \frac{10}{50} \]
\[ = \frac{1}{5} \]
**b)**
**Probability of drawing a sad or powerful card in a single draw:**
\[ P = \frac{\text{Total number of sad cards}}{\text{Total number of cards}} + \frac{\text{Total number of powerful cards}}{\text{Total number of cards}} \]
\[ = \frac{20}{50} + \frac{15}{50} \]
\[ = \frac{35}{50} \]
\[ = \frac{7}{10} \]
---
**Step 3**
**c)**
**c)**
\[ P = \left( \frac{\text{Total number of sad cards}}{\text{Total number of cards}} \right) \left( \frac{\text{Total number of lucky cards}}{\text{Total number of cards}} \right) \]
\[ = \frac{20}{50} \times \frac{10}{50} \]
\[ = \frac{2}{25} \]
Transcribed Image Text:**Probabilities and Predictions from Your Fortune Teller's Jar**
Your fortune teller’s jar contains a total of 50 cards. Each card is labeled with a predicted theme that will strongly influence how you experience the next year. The distribution of these themes is as follows:
- 10 cards are labeled “lucky”
- 20 cards are labeled “sad”
- 15 cards are labeled “powerful”
- 5 cards are labeled “kind”
**Determine the probability of drawing the following:**
a. On a single draw, a “lucky” card.
b. On a single draw, a “sad” or “powerful” card.
c. Drawing a “sad” card and then, after replacing it, a “lucky” card.
d. Drawing a sequence of “lucky”, “kind”, and “kind” (without replacement).
**Instructions:**
Calculate the probabilities using fractional form.
By understanding and calculating these probabilities, you'll gain insights into basic probability concepts, such as single events, combined events, and sequences without replacement.
Expert Solution
Step 1
Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you require the unanswered parts also, kindly re-post that parts separately.
In the given situation, there are total of 50 cards.
10 lucky cards
20 sad cards
15 powerful cards
5 kind cards
a)
The probability that drawing a lucky card is,
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