35 people coming back from America were asked if they had visited New York, Boston or San Francisco - Junior Cycle Mathematics - Question 4 - 2014

From the total of 35 people, 5 people had not visited any of the three cities. Therefore, the probability of choosing one of these people is given by:

$P(Not ext{ visited any city}) = \frac{5}{35} = \frac{1}{7}$

To find the number of people who visited New York only, we calculate:

Total who visited New York = 20 Total who visited all three cities = 7 Total who visited New York and Boston but not San Francisco = 1 Total who visited New York and San Francisco but not Boston = 3

Therefore:

People who visited just New York = 20 - (7 + 1 + 3) = 9. The probability of choosing one of these is:

$P(Visited ext{ New York only}) = \frac{9}{35}$

To find the number of people who visited either Boston or New York, we have the following:

• People who visited New York = 20
• People who visited Boston = 13
• People who visited both Boston and New York = 1 (exclusive count is needed)

Total unique visitors to Boston or New York = 20 + 13 - 1 = 32.

Therefore, the probability is:

$P(Visited ext{ Boston or New York}) = \frac{32}{35}$