Eight blue socks, six white socks, and four gray socks are mixed in a drawer. You pull out two socks, one at a time, without looking. Complete parts (a) through (d). a. Draw a tree diagram along with the possible outcomes and the probabilities of each branch. Choose the correct tree diagram below. O A. B. Oc. OD. B B -W G G B B -w -W G G G B B B -W G G .G b. What is the probability of the event of getting 2 socks of the same color? The probability is (Type an integer or a simplified fraction.)
Eight blue socks, six white socks, and four gray socks are mixed in a drawer. You pull out two socks, one at a time, without looking. Complete parts (a) through (d). a. Draw a tree diagram along with the possible outcomes and the probabilities of each branch. Choose the correct tree diagram below. O A. B. Oc. OD. B B -W G G B B -w -W G G G B B B -W G G .G b. What is the probability of the event of getting 2 socks of the same color? The probability is (Type an integer or a simplified fraction.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Title: Probability of Selecting Socks of the Same Color**
**Problem Statement:**
Eight blue socks, six white socks, and four gray socks are mixed in a drawer. You pull out two socks, one at a time, without looking. Complete parts (a) through (d).
**a. Tree Diagram**
Draw a tree diagram along with the possible outcomes and the probabilities of each branch. Choose the correct tree diagram below.
- **Diagram Options:**
- **A.** [Incorrect diagram; not described]
- **B.** [Correct diagram; as described below]
- **C.** [Incorrect diagram; not described]
- **D.** [Incorrect diagram; not described]
**Correct Tree Diagram (Option B):**
- **First Branch Level (First Sock Draw):**
- Probability of drawing a Blue sock (B): \( \frac{8}{18} \)
- Probability of drawing a White sock (W): \( \frac{6}{18} \)
- Probability of drawing a Gray sock (G): \( \frac{4}{18} \)
- **Second Branch Level (Second Sock Draw):**
- After drawing a Blue sock:
- Probability of drawing another Blue: \( \frac{7}{17} \)
- Probability of drawing a White: \( \frac{6}{17} \)
- Probability of drawing a Gray: \( \frac{4}{17} \)
- After drawing a White sock:
- Probability of drawing a Blue: \( \frac{8}{17} \)
- Probability of drawing another White: \( \frac{5}{17} \)
- Probability of drawing a Gray: \( \frac{4}{17} \)
- After drawing a Gray sock:
- Probability of drawing a Blue: \( \frac{8}{17} \)
- Probability of drawing a White: \( \frac{6}{17} \)
- Probability of drawing another Gray: \( \frac{3}{17} \)
**b. Probability Calculation**
What is the probability of the event of getting 2 socks of the same color?
The probability is: [Answer not provided; requires calculation]
**Instructions:** Type an integer or a simplified fraction for the probability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5403849-9f1b-47b1-a027-5bfd8ac96652%2F6975ecfb-8978-4b77-b51c-f810936dcd08%2Fviq0c2d_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Probability of Selecting Socks of the Same Color**
**Problem Statement:**
Eight blue socks, six white socks, and four gray socks are mixed in a drawer. You pull out two socks, one at a time, without looking. Complete parts (a) through (d).
**a. Tree Diagram**
Draw a tree diagram along with the possible outcomes and the probabilities of each branch. Choose the correct tree diagram below.
- **Diagram Options:**
- **A.** [Incorrect diagram; not described]
- **B.** [Correct diagram; as described below]
- **C.** [Incorrect diagram; not described]
- **D.** [Incorrect diagram; not described]
**Correct Tree Diagram (Option B):**
- **First Branch Level (First Sock Draw):**
- Probability of drawing a Blue sock (B): \( \frac{8}{18} \)
- Probability of drawing a White sock (W): \( \frac{6}{18} \)
- Probability of drawing a Gray sock (G): \( \frac{4}{18} \)
- **Second Branch Level (Second Sock Draw):**
- After drawing a Blue sock:
- Probability of drawing another Blue: \( \frac{7}{17} \)
- Probability of drawing a White: \( \frac{6}{17} \)
- Probability of drawing a Gray: \( \frac{4}{17} \)
- After drawing a White sock:
- Probability of drawing a Blue: \( \frac{8}{17} \)
- Probability of drawing another White: \( \frac{5}{17} \)
- Probability of drawing a Gray: \( \frac{4}{17} \)
- After drawing a Gray sock:
- Probability of drawing a Blue: \( \frac{8}{17} \)
- Probability of drawing a White: \( \frac{6}{17} \)
- Probability of drawing another Gray: \( \frac{3}{17} \)
**b. Probability Calculation**
What is the probability of the event of getting 2 socks of the same color?
The probability is: [Answer not provided; requires calculation]
**Instructions:** Type an integer or a simplified fraction for the probability.
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