In a survey of 400 tourists who visited
Egypt, 160 were from Arab countries, 120 were from Europe, 40 from Latin America, and 80
from Australia. If the total number of tourists who
visited Egypt in a month was 5000, how many of them are expected to be from Europe?
Let’s start by picking out the key
information. We’re asked about the tourists that are
from Europe. From the survey results, we can see that
120 were from Europe and that there are 400 tourists in total. So we have a fraction of 120 out of
400. Notice that even if we hadn’t been given
the value of 400, we could’ve calculated this from 160 plus 120 plus 40 plus 80. In the survey results then, we have 120
tourists out of 400 were from Europe.
We now need to expand this to work out of
the 5000 tourists in a month how many of those would be from Europe. To find this, we calculate the expected
value. This is calculated by multiplying the
probability of an event occurring by the number of trials. So therefore, to find the expected value
of tourists from Europe, we multiply the probability that a tourist is from Europe, which we
find in the experimental probability from the survey, and multiply it by the number of
tourists, which gives us 120 over 400 multiplied by 5000.
We can reduce the fraction 120 over 400
to three-tenths. And then we have a 10 on the denominator
and 5000 on the numerator. So we can cancel down to three times 500,
giving us 1500. So we would expect that out of 5000
tourists that 1500 would be from Europe.