This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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3. In a single toss of a die, the sample space is S = \1, 2, 3, 4, 5, 6\. The total number of outcomes is 6. Step 1: Identify even numbers (E). E = \2, 4, 6\ Step 2: Identify composite numbers (C). A composite number is a positive integer that has at least one divisor other than 1 and itself. C = \4, 6\ Step 3: Identify numbers that are even OR composite (E C). E C = \2, 4, 6\ The number of favorable outcomes is 3. Step 4: Calculate the probability. P(even or composite) = Number of favorable outcomesTotal number of outcomes = (3)/(6) = (1)/(2) The probability of obtaining an even number or a composite number is *(1)/(2) or 0.5. 4. To calculate the F-ratio, we perform a one-way ANOVA. Given data for 11 students across 3 subjects: Biostatistics (B): 1, 1, 0, 0, 1, 3, 0, 2, 7, 0, 0 Chemistry (C): 0, 2, 1, 1, 2, 6, 7, 3, 5, 4, 3 Biology (L): 1, 7, 5, 1, 2, 0, 4, 1, 2, 3, 0 Number of groups (k) = 3. Number of observations per group (n_j) = 11. Total number of observations (N) = 3 × 11 = 33. Step 1: Calculate sums and means for each group. B = 15 B = (15)/(11) ≈ 1.3636 C = 34 C