Respuesta :
Answer:
1. 1/12 or 0.083
2. 5/36 or 0.1389
3. 7/12 or 0.5833
4. 5/12 or 0.4167
5. 11/12 or 0.9167
6. 1/9 or 0.1111
7. 1/3 or 0.3333
8. 5/12 or 0.4167
Step-by-step explanation:
This problem can easily be understood by making sample space first.
Outcomes in sample space=S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
Total outcomes=36
The probability in the following scenario is calculated as
Probability=number of outcomes/Total outcomes
1.
The sum is 4
The sum is 4 ={(1,3),(2,2),(3,1)}
number of outcomes=3
P(The sum is 4)=3/36=1/12 or 0.083
2.
The sum is 6
The sum is 6 ={(1,5),(2,4),(3,3),(4,2),(5,1)}
number of outcomes=5
P(The sum is 6)=5/36 or 0.1389
3.
The sum is at least 7
The sum is at least 7=The sum is greater than or equal to 7
The sum is at least 7={(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,3),(4,4),(4,5),(4,6),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
number of outcomes=21
P(The sum is at least 7)=21/36
P(The sum is at least 7)=7/12 or 0.5833
4.
The sum is at least 8
The sum is at least 8=The sum is greater than or equal to 8
The sum is at least 8={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
number of outcomes=15
P(The sum is at least 8)=15/36
P(The sum is at least 8)=5/12 or 0.4167
5.
The sum is less than 11
The sum is less than 11={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(6,1),(6,2),(6,3),(6,4)}
number of outcomes=33
P(The sum is less than 11)=33/36
P(The sum is less than 11)=11/12 or 0.9167
6.
The sum is 2, 3, or 12
The sum is 2, 3, or 12={(1,1),(1,2),(2,1),(6,6)}
number of outcomes=4
P(The sum is 2, 3, or 12)=4/36
P(The sum is 2, 3, or 12)=1/9 or 0.1111
7.
The sum is odd and no more than 7
The sum is odd and no more than 7={(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(6,1)}
number of outcomes=12
P(The sum is odd and no more than 7)=12/36
P(The sum is odd and no more than 7)=1/3 or 0.3333
8.
The sum is odd or prime
The sum is odd or prime={(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}
number of outcomes=15
P(The sum is odd or prime)=15/36
P(The sum is odd or prime)=5/12 or 0.4167
Probabilities are,
1. The sum is 4 = 1/12
2. The sum is 6 = 5/36
3. The sum is at least 7 = 7/12
4. The sum is at least 8 = 5/12
5. The sum is less than 11 = 11/12
6. The sum is 2, 3, or 12 = 1/9
7. The sum is odd and no more than 7 = 1/3
8. The sum is odd or prime = 19/36
When six sided die toss two times, Then total possible Outcomes shown below
[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}[/tex]
Total number of outcomes=36
Probability is calculated by dividing number of favourable outcomes by Total number of outcomes
1. Favourable outcomes for the sum is 4 [tex]={(1,3),(2,2),(3,1)}[/tex]
number of outcomes=3
The probability of The sum is 4. = [tex]3/36=1/12 = 0.083[/tex]
2.Favourable outcomes for the sum is 6[tex]={(1,5),(2,4),(3,3),(4,2),(5,1)}[/tex]
number of outcomes=5
The probability of The sum is 6, =5/36
3.The sum is at least 7,
={(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,3),(4,4),(4,5),(4,6),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
number of outcomes=21
Probability of the sum is at least 7 =21/36=7/12 = 0.5833
4.The sum is at least 8
The sum is at least 8={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
number of outcomes=15
The sum is at least 8=15/36 = 5/12 = 0.4167
5.The sum is less than 11
The sum is less than 11={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(6,1),(6,2),(6,3),(6,4)}
number of outcomes=33
The sum is less than 11=33/36 = 11/12
6.The sum is 2, 3, or 12={(1,1),(1,2),(2,1),(6,6)}
number of outcomes=4
The sum is 2, 3, or 12=4/36 = 1/9
7.The sum is odd and no more than 7={(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(6,1)}
number of outcomes=12
The sum is odd and no more than 7=12/36 = 1/3
8.The sum is odd or prime={(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5), (3, 6), (6, 3), (4,5), (5, 4)
number of outcomes=19
The sum is odd or prime=19/36
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