Two dice are thrown. One yellow and one white. Let y be the uppermost number on the yellow die and w be the uppermost number on the white die. I’ve drawn up a table because I know that if I drop a table, the questions will be so much easier. So I do recommend all of you to drop a table before you start the question. It won’t take too long. Although it looks quite big. So all I’ve done is the yellow is from one to six, the white is from one to six. And I’ve just written out all the outcomes inside the boxes.
Starting from a! It says find probability say, probability p bracket means probability of, so just don’t forget that. So p probability of y the yellow equaling to white. So when yellow equals to white. Just pick out the outcomes and this one’s really really obvious because you can see these ones. Uh… the yellow equals to the white. They have the same outcome. And you can see it’s 6 out of the 36, so you simply simplify it to 1 over 6.
Find the probability of the sum of y and w. So when you add up the yellow outcome to the white outcome. We get seven. So I can.. have a look guys and just check and I found that these ones here. They add up to seven. So it’s simply going to be 6 out of 36 which is simplified to 1 on 6.
c! Find the probability that yellow is less than white minus two. So when I subtract two from white, I want it to be still greater than yellow. What I found were these ones here.
When I subtract two from six, I get four and the only numbers of yellow that is less than four are three two and one. And I look at the same outcomes for five when I subtract two from five, I get three sorry. And then the numbers that are less than three are just two and one. So it’s only these two and it’s this one as well. So you can apply the same way and you can check for other numbers but you’ll find that only one two three four five six of these are the outcomes that satisfy this one. So it’s just 6 over 36 which is again 1 on 6.
Now d! Find the probability that the absolute value of yellow minus w is greater or equal to two. So the reason why they have the absolute value there is because they just want you to find the difference. So even if yellow is smaller, the difference will always be positive. So even if it’s two and four or four and two, the difference is the same too. So that’s why we have the absolute value there but it’s just asking you to find the difference that makes it greater or equal to two. So again find the difference for all of these numbers and pick out the ones that are greater or equal to two. And I found that it’s these numbers on the two corners that make it greater than two because the ones in the middle here, the difference is just one or zero. So I know that the rest of them are the ones that will make two or greater. Count them up guys, one two three four five six seven eight nine ten and there’s another ten over here. So it’s 20 out of the 36 which is simplified to 5 on 9.
e! The probability that the smaller number is 5. Now I want the smaller number to be 5, so we look at this column here and this row here that has the 5. But this was easy guys because 5 is the second greatest number and the only number that’s greater than 5 is six. So it must be just these two and in these two outcomes in these two boxes 5 is a smaller number., So therefore just 2 out of 36 which is 1 on 18.
f! I want to find the probability that when I add yellow and white. It’s not equal to 5. So I must pick out the numbers that are not equal to 5. These four numbers one four and two and three they add up to 5. So I’m going to exclude those numbers and the rest of them which is 36 minus the 4, so it’s 32 out of 36 is the probability that it’s not equal to 5. So it’s simplified to 8 on 9.
g! Probability that at least one of y and w is greater than 4. So at least one of them or both of them are greater than 4. So both can be greater or just one of them can be greater. And have a look, guys! Pick out the right outcomes. I found that all of these are greater than 4. One of them or both of them are greater than 4. So it’s going to be the one two three four five six twelve plus one two three four five six seven eight. So it’s 12 plus 8 which is 20 out of 36 which is simplified to 5 on 9.
h! Probability that only one of yellow and white is greater than 4. So in the previous question, it says at least which means both of them can be greater than 4 but in this question I only want one of them to be greater than 4. So it’s going to be a lot less, it’s only going to be these ones excluding these ones. We’re not going to include these because you can see for these ones, both of them are greater than 4 but I don’t want both to be greater than 4. I only want one of them. So it’s simply going to be 16. If you count them up! You get 16. So 16 out of 36 which is 4 on 9. And that’s it, guys.
So see how that was really really easy with the table. So draw that up before you start the question, okay? I do really recommend it.
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