## Object Picking Probability - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=10, Mode=replace

 1 A bag contains 6 marbles: 1 red marble, 3 yellow marbles, and 2 blue marbles. If you take one marble out, put it back, and take another marble out, what is the probability that you'll get 1 blue marble followed by 1 red marble? 2 A bag contains 6 balls: 2 red balls, 1 yellow ball, and 3 blue balls. If you take one ball out, put it back, and take another ball out, what is the probability that you'll get 1 yellow ball followed by 1 blue ball?

### Complexity=10, Mode=no replace

 1 A bag contains 6 marbles: 1 red marble, 4 yellow marbles, and 1 blue marble. If you take one marble out, don't put it back, and take another marble out, what is the probability that you'll get 1 red marble followed by 1 yellow marble? 2 A bag contains 10 marbles: 2 red marbles, 7 yellow marbles, and 1 blue marble. If you take one marble out, don't put it back, and take another marble out, what is the probability that you'll get 1 blue marble followed by 1 yellow marble?

### Complexity=10

 1 A bag contains 8 marbles: 2 red marbles, 2 yellow marbles, and 4 blue marbles. If you take two marbles at the same time, what is the probability that you'll get 1 yellow marble and 1 blue marble? 2 A bag contains 9 balls: 4 red balls, 4 yellow balls, and 1 blue ball. If you take two balls at the same time, what is the probability that you'll get 1 blue ball and 1 yellow ball?

### Complexity=10, Mode=replace

1A bag contains 6 marbles: 1 red marble, 3 yellow marbles, and 2 blue marbles. If you take one marble out, put it back, and take another marble out, what is the probability that you'll get 1 blue marble followed by 1 red marble?
Solution
Begin by noting that since the marbles are replaced, each draw does not depend on previous draws and thus the draws are independent.
P(1 blue marble on first pick) = 2/6 = 1/3.
P(1 red marble on second pick) = 1/6.
P(picking 1 blue marble then picking 1 red marble) = (1/3) × (1/6) = 1/18
2A bag contains 6 balls: 2 red balls, 1 yellow ball, and 3 blue balls. If you take one ball out, put it back, and take another ball out, what is the probability that you'll get 1 yellow ball followed by 1 blue ball?
Solution
Begin by noting that since the balls are replaced, each draw does not depend on previous draws and thus the draws are independent.
P(1 yellow ball on first pick) = 1/6.
P(1 blue ball on second pick) = 3/6 = 1/2.
P(picking 1 yellow ball then picking 1 blue ball) = (1/6) × (1/2) = 1/12

### Complexity=10, Mode=no replace

1A bag contains 6 marbles: 1 red marble, 4 yellow marbles, and 1 blue marble. If you take one marble out, don't put it back, and take another marble out, what is the probability that you'll get 1 red marble followed by 1 yellow marble?
Solution
Begin by noting that the marbles are not replaced and thus each draw depends on previous draws. Thus the draws are dependent.
P(1 red marble on first pick) = 1/6.
P(1 yellow marble on second pick) = 4/(total marbles - 1) = 4/5.
P(picking 1 red marble then picking 1 yellow marble) = (1/6) × (4/5) = 2/15
2A bag contains 10 marbles: 2 red marbles, 7 yellow marbles, and 1 blue marble. If you take one marble out, don't put it back, and take another marble out, what is the probability that you'll get 1 blue marble followed by 1 yellow marble?
Solution
Begin by noting that the marbles are not replaced and thus each draw depends on previous draws. Thus the draws are dependent.
P(1 blue marble on first pick) = 1/10.
P(1 yellow marble on second pick) = 7/(total marbles - 1) = 7/9.
P(picking 1 blue marble then picking 1 yellow marble) = (1/10) × (7/9) = 7/90

### Complexity=10

1A bag contains 8 marbles: 2 red marbles, 2 yellow marbles, and 4 blue marbles. If you take two marbles at the same time, what is the probability that you'll get 1 yellow marble and 1 blue marble?
Solution
Ways of choosing 1 yellow marble and 1 blue marble = yellow marble # × blue marble # = 2 × 4 = 8.
Ways of choosing any 2 marbles = 8 × 7 ÷ 2 = 28.
P(choosing 1 yellow marble and 1 blue marble simultaneously) =
(Ways of choosing 1 yellow marble and 1 blue marble) / (Ways of choosing any 2 marbles) = 8/28 = 2/7.