Let's look at the possibilities:
1. Reflection along the y-axis and rotation of 180 degrees by the origin 0. (Gives us 4 and then 2 in the end)
2. Reflection along the y-axis and reflection along the x-axis. (Gives us 4 and then 3 in the end)
3. Reflection along the x-axis and rotation 90 degrees by the origin 0. (Gives us 4 and then 1 in the end)
4. Rotation of 270 degrees by the origin 0. (Gives us 2 in the end)
Option 2 is the answer.
Best of luck!
Attached you will see the solution using the trig plane and general solutions.
A) There are 36 possible outcomes.
b) The probability of a sum of 6 is 5/36.
c) She should roll a sum of 7 45 times.
d) She should roll a sum of 10 45 times.
Explanation
a) There are 6 outcomes for the first die and 6 outcomes for the second one. By the fundamental counting principle, there are 6*6 = 36 outcomes for both dice together.
b) The ways to get a sum of 6 are:
1&5; 2&4; 3&3; 4&2; 5&1. There are 5 possibilities out of a total of 36, or 5/36.
c) The ways to get a sum of 7 are:
1&6; 2&5; 3&4; 4&3; 5&2; 6&1. There are 6 out of 36, or 6/36=1/6. Since she is rolling the dice 150 times, she should get a sum of 6
1/6(150) = 150/6 = 45 times.
d) The ways to get a sum of 10 or more are:
4&6; 5&5; 6&4; 5&6; 6&5; 6&6
There are 6 ways out of 36, or 6/36 = 1/6. Since she is rolling the dice 150 times, she should get a sum of 10 or more
1/6(150) = 150/6 = 45 times.
