Video Transcript
The two-way table shows the ages and activity choices of a group of children at a summer camp. A child is selected at random. Given that this child is over 14, find the probability, to the nearest percent, that they chose climbing.
The key phrase in this problem is the little term that says “given that” because this term, so “given that,” means that it adds a condition to our probability. Because as this question tells us that, given that this child is over 14, it means that what we can do is in fact delete a whole row of our table. Because we’re not interested in the children that are 14 and under.
So we’re now only interested in these three values, which is 18, 32, and 24. So we can now say that the probability that the child chose climbing, given that they’re over 14. And I’ve shown this here using our notation for probability. And this vertical line means “given that.”
So what this is gonna be equal to is the number of children who chose climbing who are over 14, which is gonna be 32. Over the total number of children in the group of children who are over 14, which is gonna be 18 add 32 add 24, which gives us 74. So therefore, we can say that the probability the child chose climbing, given that they are over 14, is gonna be equal to 32 over 74. And this is a fraction.
However, the question asks us to give the probability to the nearest percent. So what we can do first is change our fraction into decimal by dividing 32 by 74, which gonna give us 0.4324 continued. So now to convert this into a percentage, what we’re gonna do is multiply it by 100. When you multiply a number by 100, what it means is that each of the digits is gonna move two place values to the left. And this is gonna give us 43.24 continued percent.
So now if we round this to the nearest percent, we’re gonna get 43 percent. So we can say that the probability to the nearest percent that a child chose climbing, given that they’re over 14, is 43 percent.
