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| Section | Objectives |
|---|---|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Descriptive Statistics | - Single Variable Data Analysis
|
| Probability Theory | - Probability Distributions
|
| Regression and Modeling | - Linear Relationships
|
>> Applied-Probability-and-Statistics Real Question <<
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NEW QUESTION # 68
Probability it does NOT rain = 1 # 0.25 = ?
Answer: D
Explanation:
This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
# P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.
NEW QUESTION # 69
Two independent events: P(A and B) = ?
Answer: A
Explanation:
For independent events, the probability that both events occur is the product of their individual probabilities.
The rule is P(A and B) = P(A) × P(B). Independence means that the occurrence of one event does not change the probability of the other. For example, if a coin is tossed and a die is rolled, the probability of heads and rolling a 4 is 1/2 × 1/6 = 1/12. Option B is an addition expression used in "or" problems, not "and" problems.
Option C applies to mutually exclusive events, not independent events. Option D would mean both events are certain to occur together, which is not generally true. The word "and" signals intersection, and independence allows the intersection to be calculated by multiplication. Study Guide references/topics: independent events, multiplication rule, joint probability, compound probability.
NEW QUESTION # 70
Poisson mean = 4. Probability of exactly 2 events?