Two-event conditional probability word problems (SAT). Game on.

Two-event conditional probability word problems (SAT) is a grade 10 math skill aligned to Common Core standard HSS.CP.B.6. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 two-event conditional probability word problems (sat) problems our math games drill.

CCSS HSS.CP.B.610 questions in the bank
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Warm-upeasy

In a class of 2020 students, 1212 students bring lunch from home, and 44 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 1212 students who bring lunch from home. 44 of them also bring a bottle, so P(bottle∣lunch from home)=412=13.P(\text{bottle} \mid \text{lunch from home}) = \dfrac{4}{12} = \dfrac{1}{3}\textsf{.}

Mid-gameeasy

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 66 letters with 33 A's and 22 N's. P(A first)=36P(\text{A first}) = \dfrac{3}{6} and P(N second∣A first)=25P(\text{N second} \mid \text{A first}) = \dfrac{2}{5}, so P(A then N)=36×25=15.P(\text{A then N}) = \dfrac{3}{6} \times \dfrac{2}{5} = \dfrac{1}{5}\textsf{.}

Mid-gameeasy

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 1010 letters with 33 R's. P(R first)=310P(\text{R first}) = \dfrac{3}{10} and P(R second∣R first)=29P(\text{R second} \mid \text{R first}) = \dfrac{2}{9}, so P(R then R)=310×29=115.P(\text{R then R}) = \dfrac{3}{10} \times \dfrac{2}{9} = \dfrac{1}{15}\textsf{.}

Mid-gamemedium

The letters of the word TOMORROW 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 a T?

The word TOMORROW has 88 letters with 22 R's and 11 T. P(R first)=28P(\text{R first}) = \dfrac{2}{8} and P(T second∣R first)=17P(\text{T second} \mid \text{R first}) = \dfrac{1}{7}, so P(R then T)=28×17=128.P(\text{R then T}) = \dfrac{2}{8} \times \dfrac{1}{7} = \dfrac{1}{28}\textsf{.}

Mid-gamemedium

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

The word COLOR has 55 letters with 22 O's. P(O first)=25P(\text{O first}) = \dfrac{2}{5} and P(O second∣O first)=14P(\text{O second} \mid \text{O first}) = \dfrac{1}{4}, so P(O then O)=25×14=110.P(\text{O then O}) = \dfrac{2}{5} \times \dfrac{1}{4} = \dfrac{1}{10}\textsf{.}

Mid-gamemedium

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

The word MISSISSIPPI has 1111 letters with 44 S's. P(S first)=411P(\text{S first}) = \dfrac{4}{11} and P(S second∣S first)=310P(\text{S second} \mid \text{S first}) = \dfrac{3}{10}, so P(S then S)=411×310=655.P(\text{S then S}) = \dfrac{4}{11} \times \dfrac{3}{10} = \dfrac{6}{55}\textsf{.}

Mid-gamemedium

A bag contains 66 red marbles and 44 white marbles. Two marbles are drawn one at a time without replacement. The first marble drawn is red. What is the probability that the second marble is white?

After one red marble is removed, 44 white marbles remain out of 99 marbles in the bag. So P(second white∣first red)=49.P(\text{second white} \mid \text{first red}) = \dfrac{4}{9}\textsf{.}

Buzzer beatermedium

A bag contains 44 black marbles and 66 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, 33 black marbles remain out of 99 marbles in the bag. So P(second black∣first black)=39=13.P(\text{second black} \mid \text{first black}) = \dfrac{3}{9} = \dfrac{1}{3}\textsf{.}

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Tests that cover two-event conditional probability word problems (sat):
NAEPACTSATNY State MathNJSLA
Reporting domains for this skill
SAT All grades: Problem-Solving and Data AnalysisACT All grades: Preparing for Higher MathNAEP Grade 12: Data Analysis, Statistics, and ProbabilityACT Aspire All grades: Preparing for Higher MathATLAS Algebra II: Statistics and ProbabilityCMAS High school: Statistics & Probability
More Grade 10 skills
Circle diameter endpoints to radius (SAT)Advanced area formulasCircle equation translations (ACT/SAT/PSAT 8/9/10)Normal distribution basicsUnit circle trig values (SAT)Possible coordinates on a circle (SAT)Equation of a circleMidpoint formulaAll Grade 10 practice →

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