Math Practice Online > free > lessons > Texas > 8th grade > Probability 2

These sample problems below for Probability 2 were generated by the MathScore.com engine.

## Sample Problems For Probability 2

### Complexity=5

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=6

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=7

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=8

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=9

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=10

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1.
 Probability: Odds:

2.
 Probability: Odds:

### Complexity=5

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 1/4.
P(2nd piece highlighted) = 4/5.
P(3rd piece highlighted) = 1/3.
P(all highlighted) = 1/4 × 4/5 × 1/3 = 1/15.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 1/15 = 14/15.
Odds(at least one piece unhighlighted) = 14:(15 - 14) = 14:1.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/5.
P(2nd piece highlighted) = 4/5.
P(3rd piece highlighted) = 4/5.
P(all highlighted) = 2/5 × 4/5 × 4/5 = 32/125.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 32/125 = 93/125.
Odds(at least one piece unhighlighted) = 93:(125 - 93) = 93:32.

### Complexity=6

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 3/5.
P(2nd piece highlighted) = 1/3.
P(3rd piece highlighted) = 2/4 = 1/2.
P(all highlighted) = 3/5 × 1/3 × 1/2 = 1/10.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 1/10 = 9/10.
Odds(at least one piece unhighlighted) = 9:(10 - 9) = 9:1.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/5.
P(2nd piece highlighted) = 2/6 = 1/3.
P(3rd piece highlighted) = 2/6 = 1/3.
P(all highlighted) = 2/5 × 1/3 × 1/3 = 2/45.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 2/45 = 43/45.
Odds(at least one piece unhighlighted) = 43:(45 - 43) = 43:2.

### Complexity=7

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 5/7.
P(2nd piece highlighted) = 5/6.
P(3rd piece highlighted) = 1/3.
P(all highlighted) = 5/7 × 5/6 × 1/3 = 25/126.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 25/126 = 101/126.
Odds(at least one piece unhighlighted) = 101:(126 - 101) = 101:25.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/3.
P(2nd piece highlighted) = 2/6 = 1/3.
P(3rd piece highlighted) = 3/5.
P(all highlighted) = 2/3 × 1/3 × 3/5 = 2/15.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 2/15 = 13/15.
Odds(at least one piece unhighlighted) = 13:(15 - 13) = 13:2.

### Complexity=8

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/7.
P(2nd piece highlighted) = 2/6 = 1/3.
P(3rd piece highlighted) = 1/8.
P(all highlighted) = 2/7 × 1/3 × 1/8 = 1/84.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 1/84 = 83/84.
Odds(at least one piece unhighlighted) = 83:(84 - 83) = 83:1.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 4/5.
P(2nd piece highlighted) = 1/5.
P(3rd piece highlighted) = 1/7.
P(all highlighted) = 4/5 × 1/5 × 1/7 = 4/175.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 4/175 = 171/175.
Odds(at least one piece unhighlighted) = 171:(175 - 171) = 171:4.

### Complexity=9

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 3/7.
P(2nd piece highlighted) = 1/4.
P(3rd piece highlighted) = 1/6.
P(all highlighted) = 3/7 × 1/4 × 1/6 = 1/56.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 1/56 = 55/56.
Odds(at least one piece unhighlighted) = 55:(56 - 55) = 55:1.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/3.
P(2nd piece highlighted) = 1/7.
P(3rd piece highlighted) = 5/8.
P(all highlighted) = 2/3 × 1/7 × 5/8 = 5/84.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 5/84 = 79/84.
Odds(at least one piece unhighlighted) = 79:(84 - 79) = 79:5.

### Complexity=10

Find the probability that if you randomly select one piece from each of the three shapes, you will get 3 highlighted pieces and the odds of getting at least one unhighlighted piece.
1
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 2/5.
P(2nd piece highlighted) = 1/6.
P(3rd piece highlighted) = 3/6 = 1/2.
P(all highlighted) = 2/5 × 1/6 × 1/2 = 1/30.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 1/30 = 29/30.
Odds(at least one piece unhighlighted) = 29:(30 - 29) = 29:1.
2
 Probability: Odds:

Solution
Probability that all 3 pieces are highlighted:
P(1st piece highlighted) = 3/7.
P(2nd piece highlighted) = 7/9.
P(3rd piece highlighted) = 2/3.
P(all highlighted) = 3/7 × 7/9 × 2/3 = 2/9.

Odds of choosing at least one unhighlighted piece:
P(at least one piece unhighlighted) = 1 - P(all highlighted) = 1 - 2/9 = 7/9.
Odds(at least one piece unhighlighted) = 7:(9 - 7) = 7:2.

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