Probability of rolling a sum of 9 or a sum that is even from two number cubes is 11/18 Explanation: When a dice is rolled there are different ways in which 9. can be obtained, which are (3,6) or (4,5) or (5,4) or (6,3). 4 options. As in all there are 6⋅6=36 options, probability is 4/36 or 1/9.
For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 options, probability is 18/36 or 1/2.
Note that the two events (getting 9 or even sum) are mutually exclusive, the probabilities can be just added i.e. combined probability is 1/9+1/2=2+9/18i.e. 11/18
Theta has a reference angle of 30° and is in Quadrant I or II.
Sin(theta) = ½
Basic angle: 30
<h3>What is the reference angle?</h3>
The acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive. In other words, the reference angle is an angle sandwiched between the terminal side and the x-axis.