Back to Find conditional probability from a model — Problem 1 · Task Set 23

Exercises: Find Conditional Probability as the Fraction of B's Outcomes That Are Also A

Work through each section in order. To find P(A | B), restrict to B's outcomes first, then count how many of them are also in A: the denominator is the number of B's outcomes, NOT all outcomes. Write probabilities as fractions in lowest terms unless asked otherwise, and interpret each conditional probability with a sentence: "among the B's, this fraction are A."

Grade 10·20 problems·~32 min·Common Core Math - HS Statistics and Probability·group·hss-cp-b-6

Work through problems with immediate feedback

Warm-Up: Sample Spaces and the Conditional Formula

These problems review ideas you already know from Cluster A.

A standard die is rolled, $S = \{1, 2, 3, 4, 5, 6\}$ . You are asked for $P(\text{even} \mid \text{greater than } 3)$ . When you condition on "greater than 3," what becomes the new sample space?

$\{4, 5, 6\}$ — only the outcomes greater than 3

$\{1, 2, 3, 4, 5, 6\}$ — all six outcomes, unchanged

$\{2, 4, 6\}$ — the even outcomes

$\{4, 6\}$ — the even outcomes greater than 3