unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results shown to the right. Outcome Frequency Two heads 62 a) What is the probability that both coins show heads? b) What is the probability that at least one of the coins shows heads? 106 One head, one tail Two tails c) What is the probability that the two coins show the same side? 33 O A. Subtract the probability of "two tails" from 1. O B. Divide the frequency of "two heads" by the total. C. Find the sum of the probabilities to "two heads" and "one head, one tail." O D. Find the sum of the probabilities of "two heads" and "two tails." The probability that both coins shown heads is 0.1 (Simplify your answer.) b) Let H represents heads and T represent tails. What formula should be used to find the probability that at least one of the coins shows heads? OA. P(at least one H)=P(two H) + P(two T) - P(one H, one T) O B. P(at least one H)=P(two H) + P(one H, one T) - P(two T) O C. P(at least one H) = 1 - P(two T) O D. P(at least one H)=1-(P(two H) + P(one H, one T)) The probability that at least one of the coins shows heads is 0.9 (Simplify your answer.) c) What formula should be used to find the probability that the two coins show the same side? OA. P(same side) = P(two H). P(two T) B. P(same side) = 1- (P(two H) + P(two T)) OC. P(same side) = P(two H) + P(two T) O D. P(same side) = P(two H) + P(two T) - P(one H, one T) The probability that the two coins show the same side is 0.8 (Simplify your answer)
unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results shown to the right. Outcome Frequency Two heads 62 a) What is the probability that both coins show heads? b) What is the probability that at least one of the coins shows heads? 106 One head, one tail Two tails c) What is the probability that the two coins show the same side? 33 O A. Subtract the probability of "two tails" from 1. O B. Divide the frequency of "two heads" by the total. C. Find the sum of the probabilities to "two heads" and "one head, one tail." O D. Find the sum of the probabilities of "two heads" and "two tails." The probability that both coins shown heads is 0.1 (Simplify your answer.) b) Let H represents heads and T represent tails. What formula should be used to find the probability that at least one of the coins shows heads? OA. P(at least one H)=P(two H) + P(two T) - P(one H, one T) O B. P(at least one H)=P(two H) + P(one H, one T) - P(two T) O C. P(at least one H) = 1 - P(two T) O D. P(at least one H)=1-(P(two H) + P(one H, one T)) The probability that at least one of the coins shows heads is 0.9 (Simplify your answer.) c) What formula should be used to find the probability that the two coins show the same side? OA. P(same side) = P(two H). P(two T) B. P(same side) = 1- (P(two H) + P(two T)) OC. P(same side) = P(two H) + P(two T) O D. P(same side) = P(two H) + P(two T) - P(one H, one T) The probability that the two coins show the same side is 0.8 (Simplify your answer)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![### Probability with Unfair Coins: An Educational Exercise
#### Problem Statement
Two unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results shown in the table below:
| Outcome | Frequency |
|---------------|-----------|
| Two heads | 62 |
| One head, one tail | 106 |
| Two tails | 33 |
Based on this data set, solve the following probability questions:
### Questions
**a) What is the probability that both coins show heads?**
**b) What is the probability that at least one of the coins shows heads?**
**c) What is the probability that the two coins show the same side?**
---
#### Solution Steps
**a) What is the probability that both coins show heads?**
To calculate this probability:
\[ P(\text{both heads}) = \frac{\text{Frequency of both heads outcomes}}{\text{Total trials}} \]
**Options to consider:**
- A. Subtract the probability of "two tails" from 1.
- B. Divide the frequency of "two heads" by the total.
- C. Find the sum of the probabilities to "two heads" and "one head, one tail."
- D. Find the sum of the probabilities of "two heads" and "two tails."
Based on the calculation:
The probability that both coins show heads is \(0.1\).
Correct option: **B**.
---
**b) What is the probability that at least one of the coins shows heads?**
Let H (heads) represent heads and T (tails) represent tails. We need to find the probability P(at least one H).
**Options to consider:**
- A. \( P(\text{at least one H}) = P(\text{two H}) + P(\text{two T}) - P(\text{one H, one T}) \)
- B. \( P(\text{at least one H}) = P(\text{two H}) + P(\text{one H, one T}) - P(\text{two T}) \)
- C. \( P(\text{at least one H}) = 1 - P(\text{two T}) \)
- D. \( P(\text{at least one H}) = 1 - P(\text{two H}) + P(\text{one H, one](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc56b3bff-26b7-4f28-9b8d-5c65e8bb1b58%2Fb508fc30-9eab-4f2a-baad-fc76dd148951%2Fd291zgb_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability with Unfair Coins: An Educational Exercise
#### Problem Statement
Two unfair coins, both favoring heads, are tossed simultaneously for many trials, with the results shown in the table below:
| Outcome | Frequency |
|---------------|-----------|
| Two heads | 62 |
| One head, one tail | 106 |
| Two tails | 33 |
Based on this data set, solve the following probability questions:
### Questions
**a) What is the probability that both coins show heads?**
**b) What is the probability that at least one of the coins shows heads?**
**c) What is the probability that the two coins show the same side?**
---
#### Solution Steps
**a) What is the probability that both coins show heads?**
To calculate this probability:
\[ P(\text{both heads}) = \frac{\text{Frequency of both heads outcomes}}{\text{Total trials}} \]
**Options to consider:**
- A. Subtract the probability of "two tails" from 1.
- B. Divide the frequency of "two heads" by the total.
- C. Find the sum of the probabilities to "two heads" and "one head, one tail."
- D. Find the sum of the probabilities of "two heads" and "two tails."
Based on the calculation:
The probability that both coins show heads is \(0.1\).
Correct option: **B**.
---
**b) What is the probability that at least one of the coins shows heads?**
Let H (heads) represent heads and T (tails) represent tails. We need to find the probability P(at least one H).
**Options to consider:**
- A. \( P(\text{at least one H}) = P(\text{two H}) + P(\text{two T}) - P(\text{one H, one T}) \)
- B. \( P(\text{at least one H}) = P(\text{two H}) + P(\text{one H, one T}) - P(\text{two T}) \)
- C. \( P(\text{at least one H}) = 1 - P(\text{two T}) \)
- D. \( P(\text{at least one H}) = 1 - P(\text{two H}) + P(\text{one H, one
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