Out of 250 tourists, 146 visited Korea (K), 108 visited Japan (J), 142 visited Hong Kong (H), 70 visited Korea and Japan, 71 visited Japan and Hong Kong, 82 visited Korea and Hong Kong and 46 visited Korea, Japan and Hong Kong. The Venn diagram at the right illustrates the relationship of these sets of data. If a tourist is randomly chosen from this group, what is the probability of choosing a tourist who visited a) Korea? b) Korea only? c) Japan or Hong Kong? d) Korea and Hong Kong? e) Hong Kong but not Japan? 31 K 40 36 24 46 35 25 13 H J
Answer:
a) To find the probability of choosing a tourist who visited Korea, we need to add up the number of tourists who visited Korea, including those who visited Korea alone and those who visited Korea along with other destinations. From the Venn diagram, we can see that the total number of tourists who visited Korea is 146, so the probability of choosing a tourist who visited Korea is:
Probability of choosing a tourist who visited Korea = 146/250 = 0.584
b) To find the probability of choosing a tourist who visited Korea only, we need to look at the region of the Venn diagram that represents tourists who visited Korea but did not visit Japan or Hong Kong. From the diagram, we can see that there are 46 tourists in this region. Therefore, the probability of choosing a tourist who visited Korea only is:
Probability of choosing a tourist who visited Korea only = 46/250 = 0.184
c) To find the probability of choosing a tourist who visited Japan or Hong Kong, we need to add up the number of tourists who visited Japan, the number of tourists who visited Hong Kong, and the number of tourists who visited both Japan and Hong Kong. From the Venn diagram, we can see that the total number of tourists who visited Japan or Hong Kong is:
Total number of tourists who visited Japan or Hong Kong = 108 + 142 – 71 = 179
Therefore, the probability of choosing a tourist who visited Japan or Hong Kong is:
Probability of choosing a tourist who visited Japan or Hong Kong = 179/250 = 0.716
d) To find the probability of choosing a tourist who visited Korea and Hong Kong, we simply count the number of tourists who visited both destinations. From the Venn diagram, we can see that there are 82 tourists in this region. Therefore, the probability of choosing a tourist who visited Korea and Hong Kong is:
Probability of choosing a tourist who visited Korea and Hong Kong = 82/250 = 0.328
e) To find the probability of choosing a tourist who visited Hong Kong but not Japan, we need to look at the region of the Venn diagram that represents tourists who visited Hong Kong but did not visit Japan or Korea. From the diagram, we can see that there are 25 tourists in this region. Therefore, the probability of choosing a tourist who visited Hong Kong but not Japan is:
Probability of choosing a tourist who visited Hong Kong but not Japan = 25/250 = 0.1
Answer:
a) The probability of choosing a tourist who visited Korea is the ratio of the number of tourists who visited Korea to the total number of tourists:
P(Korea) = number of tourists who visited Korea / total number of tourists
P(Korea) = 146 / 250
P(Korea) = 0.584
b) To find the probability of choosing a tourist who visited Korea only, we need to subtract the number of tourists who visited Korea and another country from the total number of tourists who visited Korea:
Number of tourists who visited Korea only = Number of tourists who visited Korea – (Number of tourists who visited Korea and Japan + Number of tourists who visited Korea and Hong Kong – Number of tourists who visited all three countries)
Number of tourists who visited Korea only = 146 – (70 + 82 – 46)
Number of tourists who visited Korea only = 40
The probability of choosing a tourist who visited Korea only is:
P(Korea only) = number of tourists who visited Korea only / total number of tourists
P(Korea only) = 40 / 250
P(Korea only) = 0.16
c) The probability of choosing a tourist who visited Japan or Hong Kong is the sum of the probabilities of choosing a tourist who visited Japan and the probability of choosing a tourist who visited Hong Kong, minus the probability of choosing a tourist who visited both countries (to avoid double-counting):
P(Japan or Hong Kong) = P(Japan) + P(Hong Kong) – P(Japan and Hong Kong)
P(Japan or Hong Kong) = 108/250 + 142/250 – 71/250
P(Japan or Hong Kong) = 0.436
d) The probability of choosing a tourist who visited Korea and Hong Kong is:
P(Korea and Hong Kong) = 82/250
P(Korea and Hong Kong) = 0.328
e) The probability of choosing a tourist who visited Hong Kong but not Japan is the number of tourists who visited Hong Kong only divided by the total number of tourists:
Number of tourists who visited Hong Kong only = Number of tourists who visited Hong Kong – (Number of tourists who visited Japan and Hong Kong + Number of tourists who visited Korea and Hong Kong – Number of tourists who visited all three countries)
Number of tourists who visited Hong Kong only = 142 – (71 + 82 – 46)
Number of tourists who visited Hong Kong only = 35
P(Hong Kong but not Japan) = number of tourists who visited Hong Kong only / total number of tourists
P(Hong Kong but not Japan) = 35/250
P(Hong Kong but not Japan) = 0.14
I HOPE YOU UNDERSTAND.
