A Pair of Fair Dice Is Tossed $$\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }$$

question 34

Essay

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the dice is 7} B: {At least one of the numbers is 3} $$\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }$$

---

Definitions:

Significance Level

A threshold for determining whether an observed effect is statistically significant, often set at 0.05.

Alternative Hypothesis

A hypothesis that contradicts the null hypothesis, proposing a new effect or relationship.

Null Hypothesis

A standard assumption that posits no meaningful difference or impact exists, usually examined in contrast with a contrasting hypothesis during statistical evaluation.

Two-sided

Pertaining to tests or intervals in statistics that consider both directions or sides of a distribution, typically involving a range of values both above and below a certain point.