Comment The trick is to know whether you should be reading your totals going down or across. We will be discussing this possibility carefully for the first question in the group.
In the meantime, letter the questions from A to H
A A is the first member of a group of 5 where you read going down. You know this because you are give the gender first and then you want the total of the people (boys and girls) who participate in this activity.
So for A you have 8 boys who will choose swimming out of 17 (the rest of course are girls). P(boy if swimming is the activity) = 8/ 17 = 0.47
B P(girl if the activity is sports) = 7/27 = 0.26 Did you catch on that you were reading down?
C P(Girl if the activity is reading) = 4/6 = 0.67
D P(Boy if the activity is sports) = 20/27 = 0.74
E This is the first question of the second group. Here you will get your totals by reading across. The reason is that you are given the activity, now you must supply the gender from the total number of people in the group of either boys or girls.
P(Swimming given that it is a girl) = 9/20 = 0.45 In other words you know you area working with girls. What you need to declare is the probability of what these girls will choose.
F P(probability of reading if it is a boy) = 2/30 = 0.07 Think very carefully how these answers are derived. It's all a matter of reading which total to take and why. In this case you are taking the total number of boys and how many of them are doing the activity.
G P(Swimming if a Boy) = 8/30 = 0.27
H P(reading if a girl) = 4/20 = 0.2
Very interesting question. You'll learn a lot if you consider which comes first and what that means.