Respuesta :
Answer:
The probability of getting two numbers whose sum is greater than 9 and less than 13 is [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
Given : A single 6-sided die is rolled twice.
To find : The probability of getting two numbers whose sum is greater than 9 and less than 13 ?
Solution :
The set of 36 equally likely outcomes,
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Getting two numbers whose sum is greater than 9 and less than 13
The favorable outcome is (4,6),(5,5),(5,6),(6, 4),(6, 5),(6, 6) = 6
The probability is given by,
[tex]\text{Probability}=\frac{\text{Favorable Outcome}}{\text{Total Outcome}}[/tex]
[tex]\text{Probability}=\frac{6}{36}[/tex]
[tex]\text{Probability}=\frac{1}{6}[/tex]
Therefore, The probability of getting two numbers whose sum is greater than 9 and less than 13 is [tex]\frac{1}{6}[/tex]
