<span>Rolling 2 6-sided dice, there are 36 outcomes in the sample space. You can list them, showing the result of the first die and then the result of the 2nd die, starting with (1,1) , (1,2), 1,3) etc until you get to (6,6).
Event A: For the sum to be less than 5, you can have the die rolls (1,1) (1,2) (1,3) (2,1), (2,2) (3,1) so there are 6 of them where you can add the rolls together and get a sum < 5. P(A) = 6/36 = 1/6.
Event B: You need a 6 on either die (or on both), so you keep the first die at 6 and run through the possibilities of the 2nd die: (6,1) (6,2) (6,3) (6,4), (6,5), (6,6). Then keep th 2nd die at 6 and go through the possiblities of the first die: (1,6) (2,6) (3,6) (4,6) (5,6) but don't list (6,6) again, we already listed it. So total there are 11 ways to get a 6 on either die or on both. To get the probability you divide 11 by the size of the sample space, so P(B) = 11/36. </span>
Ok so we can see for every 2 cups of medium coffee, the balance goes down 5.30$. So that means that for every coffee, her balance goes down 2.65$. Solving for the x-intercept means how many medium coffees can I get until my balance is 0. First, we have to find the y-int so it's easy. The slope is -2.65 because for every medium coffee, her balance goes down 2.65$. So we have y=-2.65x+b. Plugging in any point, I choose (4,14.40), we get 14.4 = -2.65 × 4 +b. Solving for b we get 25 for the y intercept, meaning the equation is y = -2.65x + 25 . To find the x intercept, we set y=0. So we have 0 = -2.65x+25. Solving for x we get approx. 9.4. We can't have decimals so we round down to 9. So the x int is ≈ 9.4 meaning we can only buy 9 coffee and have a little extra. But, if the problem said how many more coffees can she get, then here is how we do it. Since she already got 4 coffees, and the max is 9, we do 9-4 and we get 5, so she can buy 5 coffeed more.