Question

In a survey of a community, it was found that 55%

Answer 1

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 $P(A) = 0.55$

20% like winter season

This means that $P(B) = 0.2$

40% don't like both seasons

This means that 100% - 40% = 60% like at least one, which means that $P(A \cup B) = 0.6$

Proportion who like both:

This is $P(A \cap B)$. The measures are related by the following equation:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$P(A \cap B) = P(A) + P(B) - P(A \cup B)$

Using what we have

$P(A \cap B) = 0.55 + 0.2 - 0.6 = 0.15$

750 like both seasons.

This is 15% of the sample. So the total number of people is t, for which:

$0.15t = 750$

$t = \frac{750}{0.15}$

$t = 5000$

20% like winter season

Out of 5000. So

0.2*5000 = 1000

The number of people who like winter season is 1000.