The probability of an event not happening is 5. This statement means that the event would be likely to happen A) half of the time B) more than half of the time C) two-thirds of the time D) less than half of the time
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 28: Probability of an Event**
The probability of an event **not** happening is \(\frac{2}{3}\). This statement means that the event would be likely to happen:
A) half of the time
B) more than half of the time
C) two-thirds of the time
D) less than half of the time
---
**Explanation for an Educational Website:**
This question tests the understanding of basic probability concepts. The key point here is to understand what the probability of an event not happening implies about the event actually happening.
1. Probability of an event not happening is represented as \( P(A') \).
2. Given \( P(A') = \frac{2}{3} \).
3. The probability of the event **happening**, \( P(A) \), can be found by subtracting the probability of it not happening from 1, since the total probability is always 1 for all events and their complements.
\[ P(A) = 1 - P(A') = 1 - \frac{2}{3} = \frac{1}{3} \]
So, the event is likely to happen **one-third of the time**. The correct answer to choose based on the given options would be implied by understanding that if the event happens one-third of the time, it is not going to be:
A) Half of the time
B) More than half of the time
C) Two-thirds of the time
D) **Less than half of the time (Correct)**
The correct option is **D**, because one-third is indeed less than one-half.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7d0bbe2-887e-47f9-a8ca-467c2c3f1292%2F9b3736b9-5943-4b0b-9ddc-425035a9665b%2Fkssnzo_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
