Suppose a certain combination lock requires three selections of numbers, each from 0 through 34. What is the probability that a randomly selected combination has a repeated number? Give your answer as a decimal probability, not a percentage. Give your answer to exactly two decimal points.
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.
![**Problem Statement:**
Suppose a certain combination lock requires three selections of numbers, each from 0 through 34. What is the probability that a randomly selected combination has a repeated number? Give your answer as a decimal probability, not a percentage. Give your answer to exactly two decimal points.
**Your Answer:**
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**Explanation:**
This problem asks for the probability of a repeated number in a three-number sequence, each selected from the range 0 to 34. To solve this:
1. **Total Possible Combinations:** Each of the three selections can be any number from 0 to 34. Therefore, the total number of combinations is \(35 \times 35 \times 35 = 42,875\).
2. **Combinations with No Repeats:** For no repeated numbers, the first number can be any of the 35, the second any of the remaining 34, and the third any of the remaining 33. Thus, there are \(35 \times 34 \times 33 = 39,270\) combinations with no repeats.
3. **Combinations with Repeats:** Subtract the no-repeat combinations from the total combinations: \(42,875 - 39,270 = 3,605\).
4. **Probability Calculation:** The probability of a repeated number is the number of combinations with repeats divided by the total number of combinations: \(\frac{3,605}{42,875}\).
5. **Decimal Probability:** Perform the division to obtain the decimal probability, rounding to two decimal points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0758b56-2f3f-4908-9748-13b6d1596a48%2F3d3954cf-def2-4a4b-b21e-1e61f1f3109e%2Fkcj9rti_processed.jpeg&w=3840&q=75)
![Suppose 12 customers at a restaurant ordered an appetizer, 9 customers ordered a main dish, and 3 customers ordered an appetizer and a main dish. How many customers ordered an appetizer or a main dish?
Your Answer:
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