NJSLA Algebra II Conditional Probability and the Rules of Probability Practice

NJSLA Algebra II Conditional Probability and the Rules of Probability. Practice it free.

Understand independence and conditional probability and use them to interpret data; use the rules of probability to compute probabilities of compound events in a uniform probability model. This Algebra II reporting domain maps to 2 practice skills and 8 representative questions from the playable bank.

Algebra IIS-CP2 mapped skills

Conditional Probability and the Rules of Probability skills

S.CP.A.1-2 Sample spaces, independence, and conditional probability

S.CP.B.3-8 Conditional probability and compound events

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playmedium

A bag contains $4$ black marbles and $6$ white marbles. Two marbles are drawn one at a time without replacement. The first marble drawn is black. What is the probability that the second marble is also black?

After one black marble is removed, $3$ black marbles remain out of $9$ marbles in the bag. So $P(\text{second black} \mid \text{first black}) = \dfrac{3}{9} = \dfrac{1}{3}\textsf{.}$

Practice playeasy

From a table, 10 are customers who buy AND saw the ad and 25 total are customers who saw the ad. Find the conditional probability of buying given saw the ad (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{10}{25} = \dfrac{2}{5}$ .

Practice playeasy

In a class of $20$ students, $12$ students bring lunch from home, and $4$ of those students also bring a reusable water bottle. If a student who brings lunch from home is selected at random, what is the probability that the student also brings a reusable water bottle?

Restrict to the $12$ students who bring lunch from home. $4$ of them also bring a bottle, so $P(\text{bottle} \mid \text{lunch from home}) = \dfrac{4}{12} = \dfrac{1}{3}\textsf{.}$

Practice playeasy

From a table, 4 are plants that flower AND got fertilizer and 16 total are plants that got fertilizer. Find the conditional probability of flowering given fertilized (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{4}{16} = \dfrac{1}{4}$ .

Practice playeasy

The letters of the word BANANA are placed in a bag. Two letters are selected one at a time without replacement. What is the probability of drawing an A and then an N?

The word BANANA has $6$ letters with $3$ A's and $2$ N's. $P(\text{A first}) = \dfrac{3}{6}$ and $P(\text{N second} \mid \text{A first}) = \dfrac{2}{5}$ , so $P(\text{A then N}) = \dfrac{3}{6} \times \dfrac{2}{5} = \dfrac{1}{5}\textsf{.}$

Practice playeasy

From a table, 7 are games won AND played at home and 21 total are games played at home. Find the conditional probability of winning given a home game (simplified fraction).

$P(A\mid B) = \dfrac{P(A \text{ and } B)}{P(B)} = \dfrac{7}{21} = \dfrac{1}{3}$ .

Practice playeasy

The letters of the word STRAWBERRY are placed in a bag. Two letters are selected one at a time without replacement. What is the probability of drawing an R and then another R?

The word STRAWBERRY has $10$ letters with $3$ R's. $P(\text{R first}) = \dfrac{3}{10}$ and $P(\text{R second} \mid \text{R first}) = \dfrac{2}{9}$ , so $P(\text{R then R}) = \dfrac{3}{10} \times \dfrac{2}{9} = \dfrac{1}{15}\textsf{.}$

Practice playeasy

In a class, $12$ students play soccer, and $9$ of those soccer players also play chess. A soccer player is picked at random. What is the probability that they also play chess?