In a survey conducted in a neighbourhood, it was found that 25% of the residents watch movies in theaters, 35% watch movies on streaming platforms, and 15% watch movies through both theaters and streaming platforms.What is the probability that a randomly selected resident does not watch movies either in theaters or on streaming platforms?
Question
In a survey conducted in a neighbourhood, it was found that 25% of the residents watch movies in theaters, 35% watch movies on streaming platforms, and 15% watch movies through both theaters and streaming platforms.What is the probability that a randomly selected resident does not watch movies either in theaters or on streaming platforms?
Solution
To solve this problem, we first need to understand that the total probability of all possible outcomes is always 1 (or 100%). In this case, the possible outcomes are watching movies in theaters, watching movies on streaming platforms, or not watching movies at all.
From the survey, we know that:
- 25% of residents watch movies in theaters.
- 35% of residents watch movies on streaming platforms.
- 15% of residents watch movies through both theaters and streaming platforms.
However, the 15% who watch movies through both mediums are being counted twice in the above percentages. So, we need to adjust for this.
The total percentage of residents who watch movies either in theaters or on streaming platforms is therefore 25% + 35% - 15% = 45%.
Since the total probability must be 100%, the probability that a randomly selected resident does not watch movies either in theaters or on streaming platforms is 100% - 45% = 55%.
So, the probability is 55%.
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