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 6 practice skills and 8 representative questions from the playable bank.

Algebra IIS-CP6 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 playeasy

A spinner has $4$ equal sections and exactly $1$ is red. You spin it once and flip a fair coin. What is the probability of landing on red and getting heads?

Red has a probability of $1$ out of $4\textsf{,}$ or $\dfrac{1}{4}\textsf{.}$ Heads has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The events are independent, so $\dfrac{1}{4} \times \dfrac{1}{2} = \dfrac{1}{8}\textsf{.}$

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

There are $4$ posters, and $3$ will be chosen for the hallway. What is $C(4, 3)\textsf{?}$

$C(4,3) = \dfrac{4!}{3! \cdot (4-3)!} = \dfrac{24}{6 \cdot 1} = 4\textsf{.}$

Practice playeasy

A pizza shop offers $8$ toppings, and a pizza ranks $3$ of them from first to third. What is $P(8, 3)\textsf{?}$

$P(8,3) = \dfrac{8!}{5!} = \dfrac{40320}{120} = 336\textsf{.}$

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

What is $2!\textsf{?}$

$2! = 2 \times 1 = 2\textsf{.}$

Practice playeasy

A bag holds $2$ red marbles and $3$ blue marbles. You draw one marble, put it back, and draw again. What is the probability that both draws are red?

Each draw has a probability of $2$ out of $5\textsf{,}$ or $\dfrac{2}{5}\textsf{.}$ The marble is replaced, so the draws are independent: $\dfrac{2}{5} \times \dfrac{2}{5} = \dfrac{4}{25}\textsf{.}$

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 $P(\text{bottle} \mid \text{lunch from home}) = \dfrac{4}{12} = \dfrac{1}{3}\textsf{.}$