# Video: Pack 3 • Paper 3 • Question 1

Pack 3 • Paper 3 • Question 1

03:06

### Video Transcript

A bag contains red ones, blue twos, and green threes. There are two red ones. The sum of the blue numbers is six times the sum of the red numbers. The sum of the green numbers is three times the sum of the red numbers. Harpreet randomly takes a number from the bag. Work out the probability that the number is blue.

Well, the first thing we’re gonna do to actually solve this problem is have a look at the information we’ve got and see if it can help us. So first of all, we know that there are two red ones. So therefore, the sum of the red numbers is going to be one plus one, which is equal to two.

So therefore, what we’re gonna actually do is actually use this information to help us work out how many blue numbers and how many green numbers there are. And first of all, we can actually work out how many blue numbers there are, cause we’re told that the sum of the blue numbers is six times the sum of the red numbers.

Well, if the sum of the blue numbers is actually six times the sum of the red numbers, then we know that the sum of the blue numbers is gonna be equal to six multiplied by two. And that’s because we worked out that the sum of the red numbers was two, which is gonna be equal to 12.

Okay, great! So now what we can do is actually use this to find out how many blue numbers there actually are. Well, as we know from the key of the question the blue numbers are actually twos, then therefore the number of blue is gonna be equal to 12 divided by two, which is equal to six. So therefore, we know that actually there’re gonna be six blue two. So we know that we’ve got two red ones and six blue twos.

So let’s move on to our final part, which is actually to find out how many greens there are. Well, to work out how many green numbers there are, we can first of all use the fact that the sum of the green numbers is three times the sum of the red numbers. So therefore, to work this out, we’re gonna have three multiplied by two, which is gonna be equal to six. And when we look back at the question, we can see that the green numbers are actually threes. So therefore, the number of green is gonna be equal to six divided by three, which gonna be equal to two. So therefore, we know that actually there gonna be two green threes.

So now let’s actually solve the question. And the question says that it wants us to work out the probability the number is blue. So first of all, to enable us to do that, what we need to do is work out the total number of numbers. So we know that we had two red one, six blue two, and two green three. So that’s two plus six plus two. So therefore, we know that the total number of numbers is actually 10. So we’ve got 10 numbers to choose from.

So what we need to do now is work out the probability that the number is blue. So therefore, if we’re gonna work out the probability of it being blue, this is gonna be equal to six over 10. And that’s because when we work out the probability of something, if the total number of possible blue outcomes or outcomes of that thing happening — so that’s our six — divided by the total number of possible outcomes, well, in this case, there are 10 numbers, so it’ll be over 10. So therefore, if we actually divide the numerator and denominator by two, to simplify this, we gonna get that the probability that the number is blue is going to be equal to three-fifths or three over five.