Two-event conditional probability word problems practice
Two-event conditional probability word problems is a grade 7 math skill aligned to Common Core standard 7.SP.C.8: find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 two-event conditional probability word problems problems our math games drill.
CCSS 7.SP.C.810 questions in the bank
Sample questions
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Question 1easy
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(bottle∣lunch from home)=124=31.
Question 2easy
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(A first)=63 and P(N second∣A first)=52, so P(A then N)=63×52=51.
Question 3easy
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(R first)=103 and P(R second∣R first)=92, so P(R then R)=103×92=151.
Question 4medium
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 8 letters with 2 R's and 1 T. P(R first)=82 and P(T second∣R first)=71, so P(R then T)=82×71=281.
Question 5medium
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 5 letters with 2 O's. P(O first)=52 and P(O second∣O first)=41, so P(O then O)=52×41=101.
Question 6medium
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 11 letters with 4 S's. P(S first)=114 and P(S second∣S first)=103, so P(S then S)=114×103=556.
Question 7medium
A bag contains 6 red marbles and 4 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, 4 white marbles remain out of 9 marbles in the bag. So P(second white∣first red)=94.
Question 8medium
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(second black∣first black)=93=31.
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