Probability and Statistics
Problems related to probability distributions, statistical inference, data analysis, etc.
Problems in this category
The problem asks us to calculate the standard deviation of the numbers 15, 21, 17, 26, 18, and 29, g...
Standard DeviationStatisticsData Analysis
2025/4/10
The problem consists of two parts. Part 1: Given $P(\overline{A}) = 0.3$, $P(B) = 0.4$, and $P(A \ca...
Conditional ProbabilitySet TheoryProbability Rules
2025/4/10
The problem provides a table showing the distribution of marks scored by students. The marks range f...
MeanInterquartile RangeProbabilityData AnalysisFrequency Distribution
2025/4/10
A machine has a 95% chance of being properly adjusted each morning. When properly adjusted, the prod...
Bayes' TheoremConditional ProbabilityProbabilityTotal Probability
2025/4/10
We are given that out of 120 customers, 45 bought both bags and shoes. All customers bought either b...
Venn DiagramsSet TheoryProbabilityWord Problems
2025/4/10
We need to prove the Law of Total Probability, which states that if events $B_1, B_2, ..., B_n$ form...
ProbabilityLaw of Total ProbabilityConditional ProbabilitySet Theory
2025/4/9
The image provides a formula for calculating the probability of an event $A$, denoted as $P(A)$, usi...
ProbabilityLaw of Total ProbabilityConditional ProbabilityEvents
2025/4/9
The image describes the Law of Total Probability. Given a sample space $S$ of an experiment $E$, an...
ProbabilityLaw of Total ProbabilityConditional ProbabilityEventsSample SpacePartition
2025/4/9
We are given two sets of numbers. We need to find the five-number summary (minimum, first quartile, ...
Descriptive StatisticsFive-Number SummaryQuartilesMedianData Analysis
2025/4/8
The problem is to create a box plot for the dataset {9, 15, 19, 5, 20, 15}. We need to order the dat...
Box PlotData AnalysisQuartilesMedianDescriptive Statistics
2025/4/8