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MATH-C07-C-001
The odd die outcomes are 1, 3, and 5.
MATH-C07-C-002
Use 1 - P(A).
MATH-C07-C-003
Add the three probabilities.
MATH-C07-C-004
Compute 2(0.25) + 6(0.75).
MATH-C07-C-005
Standard deviation is the square root of variance.
MATH-C07-C-006
The two flips are independent.
MATH-C07-C-007
Use P(A | B) = P(A and B) / P(B).
MATH-C07-C-008
Use (P(B | A)P(A)) / P(B).
MATH-C07-C-009
A yes/no outcome is binary.
MATH-C07-C-010
Co-movement is not the same as causation.
MATH-C07-C-011
The labels are not equally likely, so add probability mass instead of counting labels.
MATH-C07-C-012
Use the addition rule with overlap: P(A or B) = P(A) + P(B) - P(A and B).
MATH-C07-C-013
A mini-batch is a sample from a larger data-generating process.
MATH-C07-C-014
The numerator is joint probability. Conditional probability divides by the probability of the condition.