The question is "what is the probability that a randomly selected student was certain or believes the balloon will shrink?"
There are two components to this question:
(A) People that are certain
(B) People who believe the balloon will shrink
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Focus on aspect (A) for now. So that means highlight the values in the "certain" row, which is row 1. Add up these values: 9+8+6 = 17+6 = 23. There are 23 people who are certain.
Now move onto aspect (B). Highlight the "shrink" column which is column 1. Add up the values: 9+4 = 13. There are 13 people who believe it will shrink.
There are 23+13 = 36 people who either (A) are certain or (B) believe it will shrink and 9 who fit both (A) and (B). Subtract out these 9 because they are double-counted. So we go from 36 to 36-9 = 27
Overall there are 27 people that either are certain, believe the balloon will shrink, or fit both categories.
This is out of 38 students total (add up all the values shown in the table).
Divide those two values: 27/38
We reduce if possible. In this case, we cannot reduce as 27 and 38 have no common factors
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The final answer is the fraction 27/38
