Red snapper is a rare and expensive reef fish served at upscale restaurants. A certain law prohibits restaurants from serving a cheaper, look-alike variety of fish (vermilion snapper or lane snapper) to customers who order red snapper. Researchers at a university used DNA analysis to examine fish specimens labeled "red snapper" that were purchased form vendors across the country. The DNA tests revealed that 65% of the specimens were not red snapper, but the cheaper, look-alike variety of fish.
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.
![### Understanding the Probability of Being Served Authentic Red Snapper
Red snapper is a rare and expensive reef fish typically found in upscale restaurants. There is a law that prohibits restaurants from serving cheaper look-alike fish species (vermilion snapper or lane snapper) to customers who order red snapper. Researchers conducted a DNA analysis on fish specimens labeled “red snapper” purchased from various vendors across the country. This study revealed that 65% of these labeled specimens were actually not red snapper, but a cheaper alternative.
#### Probability Questions
**a. What is the probability that you are served genuine red snapper the next time you order it at a restaurant?**
Given the study's findings, we know that only 35% of the samples were authentic red snapper. Hence, the probability can be calculated as:
\[ \text{Probability} = 0.35 \]
This probability should be rounded to the nearest hundredth.
**The probability is [ ] (Round to the nearest hundredth as needed).**
**b. If there are five customers at a restaurant, all of whom have ordered red snapper, what is the probability that at least one customer is actually served red snapper?**
To find this probability, we first calculate the complementary event: none of the five customers being served red snapper. The probability of not getting red snapper in a single order is 0.65 (since 65% are not red snapper).
\[ P(\text{Not served red snapper}) = 0.65 \]
For five customers,
\[ P(\text{None served red snapper}) = 0.65^5 \]
Hence, the probability that at least one customer is served red snapper is:
\[ P(\text{At least one served red snapper}) = 1 - P(\text{None served red snapper}) \]
This probability should be rounded to four decimal places.
**The probability is [ ] (Round to four decimal places as needed).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd210f98b-1208-4eea-a54e-043fbbd49724%2F2315dfa5-f3dc-4719-8afc-fe6c96dad810%2Fary9ckt.png&w=3840&q=75)
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