Question

the estimated percent distribution of a certain countrys population for 2025 is shown in the accompanying pie chart. find the probability of each event listed in parts (a) through (d) below
click the icon to view the pie chart.
(a) randomly selecting someone who is under 5 years old
the probability is
(round to one decimal place as needed.)
(b) randomly selecting someone who is 45 years old or over
the probability is
(round to one decimal place as needed.)
(c) randomly selecting someone who is not 65 years old or over
the probability is
(round to one decimal place as needed.)
(d) randomly selecting someone who is between 20 and 34 years old
the probability is
(round to one decimal place as needed.)

Explanation:

Step1: Solve (a)

The probability of randomly selecting someone who is under 5 years old is directly given as \(5.6\%\) in the pie - chart.

Step2: Solve (b)

For someone who is 45 years old or over, we add the percentages of \(45 - 64\) years (\(25.5\%\)), \(65 - 74\) years (\(9.2\%\)) and \(75\) years or over (\(7.2\%\)).

$$25.5\%+9.2\% + 7.2\%=41.9\%$$

Step3: Solve (c)

The probability of being 65 years old or over is \(9.2\%+7.2\% = 16.4\%\). Using the complement rule \(P(\text{not }A)=1 - P(A)\), the probability of not being 65 years old or over is \(100\%-(9.2\% + 7.2\%)=83.6\%\)

Step4: Solve (d)

For someone between 20 and 34 years old, we add the percentages of \(20 - 24\) years (\(6.8\%\)) and \(25 - 34\) years (\(13.7\%\))

$$6.8\%+13.7\%=20.5\%$$

Answer:

(a) \(5.6\%\)
(b) \(41.9\%\)
(c) \(83.6\%\)
(d) \(20.5\%\)