Ninety-three countries won medals at the Olympics in a particular year. The results indicate the following.
1 country won more than 100 medals
5 countries won between 51 and 100 medals
4 countries won between 31 and 50 medals
3 countries won between 21 and 30 medals
10 countries won between 11 and 20 medals
19 countries won between 6 and 10 medals
51 countries won between 1 and 5 medals
Suppose one of the 93 countries winning medals at this Olympics is selected at random. (Round your answers to four decimal places.)
(a) What is the probability that the selected country won more than 50 medals?
(b) What is the probability that the selected country did not win more than 100 medals?
(c) What is the probability that the selected country won 10 or fewer medals?
(d) What is the probability that the selected country won between 11 and 50 medals?
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(a) There are a total of 93 countries that won medals. From the given information, we know that 1 country won more than 100 medals, 5 countries won between 51 and 100 medals, and 4 countries won between 31 and 50 medals. Therefore, the total number of countries that won more than 50 medals is 1 + 5 + 4 = 10.
The probability that the selected country won more than 50 medals is 10/93 = 0.1075.
(b) The probability that the selected country did not win more than 100 medals is 1 - (1/93) = 92/93 = 0.9892.
(c) From the given information, we know that 10 countries won between 11 and 20 medals, 19 countries won between 6 and 10 medals, and 51 countries won between 1 and 5 medals. Therefore, the total number of countries that won 10 or fewer medals is 10 + 19 + 51 = 80.
The probability that the selected country won 10 or fewer medals is 80/93 = 0.8602.
(d) From the given information, we know that 4 countries won between 31 and 50 medals, 3 countries won between 21 and 30 medals, 10 countries won between 11 and 20 medals, and 19 countries won between 6 and 10 medals. Therefore, the total number of countries that won between 11 and 50 medals is 4 + 3 + 10 + 19 = 36.
The probability that the selected country won between 11 and 50 medals is 36/93 = 0.3871.
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