Question

In a survey, 60% of interviewees say they like beach sports, while 55% like mountain sports. If 20% like both, what fraction of the interviewees likes neither? Write your answer as a decimal rounding to the next hundredth if needed.

Answer 1

Answer:

0.05

Step-by-step explanation:

To solve this problem, we first need to calculate the percentage of people that like beach or mountain sports.

This percentage can be calculated with the formula:

P(M or B) = P(M) + P(B) - P(M and B)

where:

P(M or M) is the percentage of people that like beach or mountain sports,

P(B) is the percentage of people that like beach sports,

P(M) is the percentage of people that like mountain sports,

P(B) is the percentage of people that like beach and mountain sports.

Then:

P(M or B) = 0.55 + 0.60 - 0.20 = 0.95

95% of the people like mountain or beach sport. Now, to find the percentage of people that like neither, we just need to make 1 minus the percentage of people that like beach or mountain sports:

P(Neither) = 1 - P(M or B) = 1 - 0.95 = 0.05

0.05 or 5% of the people interviewed like neither of these sports.

Answer 2

Answer:

0.05

Step-by-step explanation:

According to the question,a survey took place and 60% of interviewees say they like beach sports, while 55% like mountain sports. If 20% like both, what fraction of the interviewees likes neither?

If 60% of them like beach sports,55% like mountain sports and 20% enjoy both.

With the above information, we need to find the percentages of interviewees that like only beach sports and mountain sports respectively.

Since 60% like beach sports and we know that in that 60% of people,20% also like mountain sports.So the percentage of people that like only beach sports is 60 - 20 = 40%

Do same for mountain sports lovers only and we have 35% of them.

Now we have 40% of beach sports lovers,35% of mountain sports lovers and 20% lovers of both sports.

This percentages gives us a total of 95% and the remaining percentage (5%) do not like either sport.

5/100 of them = 0.05