Question

A survey was conducted with 100 people. 20% said they liked Star Trek , 75% said they liked Star Wars, and 10% said they liked both. If one person is chosen at random, find the probability they either liked both or neither movies.

Answer 1

The probability is 1/4 or 25%

Explanation:

Since 100% matches the 100 value, we can have the percentage as the number of people that actually likes a particular movie

This mean; 20 people liked star Trek, 75 people liked Star wars and 10 people liked both

Let the number of people that liked neither be x

Mathematically, we can have the sum as follows for the set notation;

100 = (75-10) + (20-10) + 10 + x

100 = 65 + 10 + 10 + x

100 = 85 + x

x = 100-85

x = 15

What this mean is that 15 persons liked neither

The probability of selecting a random that likes both movies is simply the number of people that liked both/total number of people on the survey

Mathematically, that will be 10/100 = 1/10

For the probability that likes neither, we have the number that liked neither as 15

So the probability of selecting someone from here is 15/100 = 3/20

Since we have or between both probabilities, we will need to add both

So, mathematically, we have it that;

3/20 + 1/10 = (3 + 2)/20 = 5/20 = 1/4 or simply 25%