A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are
I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric Train
Choose the following statements about the probabilities of preschool television viewing that are correct.
68% of the preschoolers watched Little Galileo
31.5% of preschoolers do NOT watch Super Reader
67.5% of preschoolers only watch Prehistoric Train.
89% of the preschoolers watch Little Galileo, Super Reader, or Prehistoric Train.
35.4% of preschoolers who watch a show watch Super Reader.
22% of preschoolers do NOT watch Little Galileo, Super Reader or Prehistoric Train.
7% of preschoolers only watch Prehistoric Train and Super Reader.
23.6% of preschoolers who watch a show watch Little Galileo.
68.5% of the preschoolers do NOT watch Super Reader
75.8% preschoolers who watch a show, do NOT watch Prehistoric Train.
what is the answer
To answer these statements about the probabilities of preschool television viewing, we need to analyze the information provided in the study.
Statement 1: 68% of the preschoolers watched Little Galileo.
To determine the percentage, we need to calculate the number of preschoolers who watched Little Galileo and divide it by the total number of preschoolers.
Number of preschoolers who watched Little Galileo = 136
Total number of preschoolers = 200
Percentage = (136 / 200) * 100 = 68%
Therefore, this statement is correct.
Statement 2: 31.5% of preschoolers do NOT watch Super Reader.
To determine the percentage, we need to calculate the number of preschoolers who do not watch Super Reader and divide it by the total number of preschoolers.
Number of preschoolers who do not watch Super Reader = 200 - (63 + 14) = 200 - 77 = 123
Total number of preschoolers = 200
Percentage = (123 / 200) * 100 = 61.5%
Therefore, this statement is incorrect.
Statement 3: 67.5% of preschoolers only watch Prehistoric Train.
To determine the percentage, we need to calculate the number of preschoolers who only watch Prehistoric Train and divide it by the total number of preschoolers.
Number of preschoolers who only watch Prehistoric Train = 31
Total number of preschoolers = 200
Percentage = (31 / 200) * 100 = 15.5%
Therefore, this statement is incorrect.
Statement 4: 89% of the preschoolers watch Little Galileo, Super Reader, or Prehistoric Train.
To determine the percentage, we need to calculate the number of preschoolers who watch at least one of the given shows and divide it by the total number of preschoolers.
Number of preschoolers who watch at least one of the given shows = (136 + 14 + 31) = 181
Total number of preschoolers = 200
Percentage = (181 / 200) * 100 = 90.5%
Therefore, this statement is incorrect.
Statement 5: 35.4% of preschoolers who watch a show watch Super Reader.
To determine the percentage, we need to calculate the number of preschoolers who watch Super Reader out of those who watch any of the given shows.
Number of preschoolers who watch Super Reader = 63
Number of preschoolers who watch at least one of the given shows = 181
Percentage = (63 / 181) * 100 = 34.8%
Therefore, this statement is incorrect.
Statement 6: 22% of preschoolers do NOT watch Little Galileo, Super Reader or Prehistoric Train.
To determine the percentage, we need to calculate the number of preschoolers who do not watch any of the given shows and divide it by the total number of preschoolers.
Number of preschoolers who do not watch any of the given shows = 22
Total number of preschoolers = 200
Percentage = (22 / 200) * 100 = 11%
Therefore, this statement is incorrect.
Statement 7: 7% of preschoolers only watch Prehistoric Train and Super Reader.
To determine the percentage, we need to calculate the number of preschoolers who only watch Prehistoric Train and Super Reader, and then divide it by the total number of preschoolers.
Number of preschoolers who only watch Prehistoric Train and Super Reader = 14
Total number of preschoolers = 200
Percentage = (14 / 200) * 100 = 7%
Therefore, this statement is correct.
Statement 8: 23.6% of preschoolers who watch a show watch Little Galileo.
To determine the percentage, we need to calculate the number of preschoolers who watch Little Galileo out of those who watch any of the given shows.
Number of preschoolers who watch Little Galileo = 136
Number of preschoolers who watch at least one of the given shows = 181
Percentage = (136 / 181) * 100 = 75.1%
Therefore, this statement is incorrect.
Statement 9: 68.5% of the preschoolers do NOT watch Super Reader.
To determine the percentage, we need to calculate the number of preschoolers who do not watch Super Reader and divide it by the total number of preschoolers.
Number of preschoolers who do not watch Super Reader = 123
Total number of preschoolers = 200
Percentage = (123 / 200) * 100 = 61.5%
Therefore, this statement is incorrect.
Statement 10: 75.8% of preschoolers who watch a show, do NOT watch Prehistoric Train.
To determine the percentage, we need to calculate the number of preschoolers who watch any of the given shows but do not watch Prehistoric Train, and then divide it by the total number of preschoolers who watch any of the given shows.
Number of preschoolers who watch any of the given shows but do not watch Prehistoric Train = (63 + 14) = 77
Number of preschoolers who watch at least one of the given shows = 181
Percentage = (77 / 181) * 100 = 42.5%
Therefore, this statement is incorrect.
Based on the analysis, the correct statements about the probabilities of preschool television viewing are:
Statement 1: 68% of the preschoolers watched Little Galileo.
Statement 7: 7% of preschoolers only watch Prehistoric Train and Super Reader.
Draw your Venn diagram. If
x = # who watched Galileo & Reader
y = # who watched all three shows
t = # who watched only Train
r = # who watched only Reader
then we know that
73+x+y+31 = 136
x+y+r+14 = 63
73+x+r+22 = 135
73+x+r+y+31+14+t = 200-22
Simplifying all those, we get
x+y = 32
x+y+r = 49
x+r = 40
x+y+r+t = 60
Now we can substitute x+r=40 and x+y=32, to get
r = 17
y = 9
t = 11
so, x = 23
Now you can check the statements