Question Video: Calculating a Conditional Probability from a Two-Way Frequency Table Statistics • Third Year of Secondary School

Video Transcript

The two way table shows the ages and activity choices of a group of participants at a summer camp. A child is selected at random. Given that they chose abseiling, find the probability that the child is over 14.

Let’s go ahead and let event 𝐴 be to choose abseiling and event 𝐵 to be a child over 14. So it says, it’s given that they chose abseiling. Find the probability that the child is over 14. So we wanna know the probability of 𝐵, given that 𝐴 happened.

And the formula for the probability of 𝐵 given 𝐴 is: the probability of 𝐴 and 𝐵 divided by the probability of 𝐴. So the probability of 𝐴 and 𝐵, so choosing abseiling and being over 14 would be 24. Now the probability of 𝐴, so just of abseiling, how many people chose abseiling? Well, that would be 24 plus eight, so 32 total.

24 divided by 32 is 0.75 which would be 75 percent.