sea has five nickels, three dimes, and seven pennies in his pocket. If he randomly Ks 2 coins without replacement, what is the probability of him choosing a nickel na penny? 1/6 1/7 7/45 1/15
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![### Question:
Hosea has five nickels, three dimes, and seven pennies in his pocket. If he randomly picks 2 coins without replacement, what is the probability of him choosing a nickel then a penny?
### Options:
- ⬜ 1/6
- ⬜ 1/7
- ⬜ 7/45
- ⬜ 1/15
### Explanation:
To find the probability of Hosea picking a nickel first and then a penny, we can follow these steps:
1. **Total Coins**: There are \(5 + 3 + 7 = 15\) coins in total.
2. **Probability of Picking a Nickel First**:
The probability of picking a nickel first is the ratio of the number of nickels to the total number of coins initially, which is \( \frac{5}{15} \).
3. **Probability of Picking a Penny Second**:
After one nickel is picked, there are now 14 coins left. Since one of those picked isn't a penny, all 7 pennies would still be available.
The probability of picking a penny is the ratio of the number of pennies to the remaining coins, which is \( \frac{7}{14} \).
4. **Combined Probability**:
To find the combined probability of both events (selecting a nickel first and then a penny), multiply the two probabilities together:
\[
\frac{5}{15} \times \frac{7}{14} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
\]
**Therefore, the probability that Hosea picks a nickel and then a penny without replacement is \( \frac{1}{6} \). The correct answer is 1/6.**
### Final Answer:
- ✅ 1/6
- ⬜ 1/7
- ⬜ 7/45
- ⬜ 1/15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5161d0-8c1c-4aef-9d6c-2e647d1b4222%2F8dd25638-4fe4-4e57-b636-3be03cc462c7%2Fez1dkjd4_processed.jpeg&w=3840&q=75)
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