This technical Probability and Statistics exercise presents a set of Python code fragments designed to demonstrate basic probability calculations and statistical hypothesis testing. The material is organised as a jigsaw-style collection of code segments, allowing the underlying logical sequence to be reconstructed from variable definitions, probability calculations, observed data, statistical testing and final interpretation. Jigsaw_Puzzle_3_Original_Struct… The first part models a two-bag probability problem. Bag 1 contains four white and two black items, while Bag 2 contains three white and five black items. The code calculates the probabilities of selecting a white or black item from each bag and then uses multiplication rules to determine the probability of drawing two white items, two black items, or one white and one black item across the two bags. Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… A second section demonstrates a chi-square test of independence using an observed frequency table containing grade outcomes for girls and boys across grades A, B, C and D. The data are stored in a NumPy array and analysed using SciPy's chi2_contingency function. The resulting chi-square statistic, p-value, degrees of freedom and expected frequencies are calculated and displayed. Jigsaw_Puzzle_3_Original_Struct… Jigsaw_Puzzle_3_Original_Struct… The final fragment applies a conventional significance threshold of α = 0.05. If the p-value is greater than 0.05, the code reports that the null hypothesis should not be rejected; otherwise, it concludes that a statistically significant difference exists. Jigsaw_Puzzle_3_Original_Struct… Overall, the document demonstrates core statistical-programming concepts including probability rules, contingency tables, chi-square analysis, expected frequencies, p-value interpretation and hypothesis testing using Python, NumPy and SciPy. Important: because this file does not identify a university, module, academic level, academic year, assignment brief, formal word count or referencing system, I would leave those fields as Not specified rather than guessing.
Probability · Statistics · Python · NumPy · SciPy · Chi-Square Test · Chi-Square Test of Independence · Contingency Table · Hypothesis Testing · P-Value · Expected Frequencies · Null Hypothesis
Megaminds has supported academic requirements in probability and statistics / data analysis / python and related disciplines.