Answered

Find the best solutions to your problems with the help of IDNLearn.com. Explore a wide array of topics and find reliable answers from our experienced community members.

[-/2 Points]

DETAILS

The silver urn contains eight black balls and nine brown balls. The golden urn contains four red balls, three yellow balls, and three blue balls. If I choose a ball from the silver urn and a ball from the golden urn, what is the probability that I get a black ball and a red ball? Express your answer as a decimal rounded to 3 decimal places.

Submit Answer

---

[2/2 Points]

DETAILS

A new college graduate leaves a job interview and says there is a 120% chance that she will get the job. Choose the most appropriate response below.

A. 120% is not possible. The graduate is emphasizing that she is certain to get the job.

Sagot :

GinnyAnsweridn
Alright, let's break down the given problem step-by-step to find the required probabilities.

### 1. Describing the Contents of Each Urn
We have:
- Silver Urn: 8 black balls and 9 brown balls.
- Golden Urn: 4 red balls, 3 yellow balls, and 3 blue balls.

### 2. Calculating the Total Number of Balls in Each Urn
First, let's calculate the total number of balls in each urn:
- Silver Urn: [tex]\(8 + 9 = 17\)[/tex] balls.
- Golden Urn: [tex]\(4 + 3 + 3 = 10\)[/tex] balls.

### 3. Finding Individual Probabilities
#### Probability of Picking Each Type of Ball from the Silver Urn
- Probability of picking a black ball from the silver urn:
[tex]\[ \text{P(Black)} = \frac{8}{17} \][/tex]

- Probability of picking a brown ball from the silver urn:
[tex]\[ \text{P(Brown)} = \frac{9}{17} \][/tex]

#### Probability of Picking Each Type of Ball from the Golden Urn
- Probability of picking a red ball from the golden urn:
[tex]\[ \text{P(Red)} = \frac{4}{10} = 0.4 \][/tex]

- Probability of picking a yellow ball from the golden urn:
[tex]\[ \text{P(Yellow)} = \frac{3}{10} = 0.3 \][/tex]

### 4. Calculating Combined Probabilities
#### Probability of Picking a Black Ball from the Silver Urn and a Red Ball from the Golden Urn
[tex]\[ \text{P(Black and Red)} = \left(\frac{8}{17}\right) \times 0.4 \][/tex]

#### Probability of Picking a Brown Ball from the Silver Urn and a Yellow Ball from the Golden Urn
[tex]\[ \text{P(Brown and Yellow)} = \left(\frac{9}{17}\right) \times 0.3 \][/tex]

### 5. Adding the Combined Probabilities
To answer the question, we need the total probability of either event occurring:
[tex]\[ \text{Total Probability} = \text{P(Black and Red)} + \text{P(Brown and Yellow)} \][/tex]

### 6. Results
- The probability that we get a black ball from the silver urn and a red ball from the golden urn is:
[tex]\[ \boxed{0.188} \][/tex]

- The probability that we get a brown ball from the silver urn and a yellow ball from the golden urn is:
[tex]\[ \boxed{0.159} \][/tex]

- The total probability that either of these events occurs is:
[tex]\[ \boxed{0.347} \][/tex]

Thus, the final answer to the question about the probability of either getting a black ball from the silver urn and a red ball from the golden urn, or a brown ball from the silver urn and a yellow ball from the golden urn, is [tex]\(0.347\)[/tex] rounded to three decimal places.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.