Respuesta :
Answer:
The number of people who like winter season is 1000.
Step-by-step explanation:
Event event correspond to a set in the Venn diagram, and we use it to find the percentages.
I am going to say that:
Event A: Like summer season
Event B: Like winter season.
55% like summer season
This means that [tex]P(A) = 0.55[/tex]
20% like winter season
This means that [tex]P(B) = 0.2[/tex]
40% don't like both seasons
This means that 100% - 40% = 60% like at least one, which means that [tex]P(A \cup B) = 0.6[/tex]
Proportion who like both:
This is [tex]P(A \cap B)[/tex]. The measures are related by the following equation:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
Using what we have
[tex]P(A \cap B) = 0.55 + 0.2 - 0.6 = 0.15[/tex]
750 like both seasons.
This is 15% of the sample. So the total number of people is t, for which:
[tex]0.15t = 750[/tex]
[tex]t = \frac{750}{0.15}[/tex]
[tex]t = 5000[/tex]
20% like winter season
Out of 5000. So
0.2*5000 = 1000
The number of people who like winter season is 1000.
