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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.