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.

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.

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