For his homework, Larson was asked to find out which of his 30 classmates had a television in their rooms and record their gender. Larson did not record his own data. His results are given below. 20 of his classmates do not have a television in their room. Five of the girls have a television in their room. 13 of Larson’s classmates are boys. Part a) Use Larson’s results to complete the frequency tree.
A frequency tree is similar to a tree diagram, except instead of writing in the probabilities, we write the frequencies. Larson had a total of 30 classmates. Therefore, 30 goes in the first box. Of these 30 classmates, we were told that 20 do not have a television in their room.
To calculate the number of classmates who do have a television, we need to subtract 20 from 30. 30 minus 20 is equal to 10. Therefore, 10 of his classmates have a television in their room.
We were also told that five of the girls have a television in their room. This means that five out of the 10 students with a TV are female. 10 minus five is equal to five. Therefore, there must be five male students with a TV in their room.
Finally, we were told that 13 of Larson’s classmates are boys. To work out the number of males who did not have a TV in their room, we need to subtract five from 13. This is equal to eight. There are eight males that do not have a TV. As there were 13 boys, there must be a total of 17 girls as 30 minus 13 is equal to 17. 17 minus five is equal to 12. Therefore, there are 12 females who do not have a TV.
We can check these numbers by ensuring that all the answers in each step of the frequency tree add up to 30. In this case, 10 plus 20 is equal to 30. And also, five plus five plus eight plus 12 is equal to 30. We, therefore, have a completed frequency tree for Larsson’s results.
The second part of the question says the following.
One of the classmates who has a television in their room is chosen at random. Part b) What is the probability that they are female? There were a total of 10 people that had a television in their room. Of these, five were male and five were female. This means that the probability of one of those 10 students being female is five out of 10 or five tenths.
This can be simplified to one-half by dividing the numerator and denominator by five. Remember with fractions, whatever you do to the top, you must do to the bottom. If one of the classmates with a television is chosen at random, the probability that they are female is one-half. This could also be written as 0.5 or 50 percent.