Questions: The age distribution for politicians in a certain country is shown in the accompanying table. Suppose that a politician is selected at random. Let events A, B, C, and S be defined as follows. Complete parts (a) through (d) below. A= event the politician is under 50 B= event the politician is in his or her 50 s C= event the politician is in his or her 60 s S= event the politician is under 70 Click the icon to view the number of politicians in each age bracket. a. Use the table and the f / N rule to find P(S). P(S)= (Type an integer or a decimal. Round to three decimal places as needed.) Number of Politicians Per Age Bracket Age (yr) No. of politicians Under 50 11 50-59 29 60-69 42 70-79 19 80 and over 3

The age distribution for politicians in a certain country is shown in the accompanying table. Suppose that a politician is selected at random. Let events A, B, C, and S be defined as follows. Complete parts (a) through (d) below.

A= event the politician is under 50
B= event the politician is in his or her 50 s
C= event the politician is in his or her 60 s
S= event the politician is under 70
Click the icon to view the number of politicians in each age bracket.
a. Use the table and the f / N rule to find P(S).
P(S)=  (Type an integer or a decimal. Round to three decimal places as needed.)

Number of Politicians Per Age Bracket
Age (yr)  No. of politicians 
Under 50  11 
50-59  29 
60-69  42 
70-79  19 
80 and over  3
Transcript text: The age distribution for politicians in a certain country is shown in the accompanying table. Suppose that a politician is selected at random. Let events A, B, C, and S be defined as follows. Complete parts (a) through (d) below. $A=$ event the politician is under 50 $B=$ event the politician is in his or her 50 s $\mathrm{C}=$ event the politician is in his or her 60 s $\mathrm{S}=$ event the politician is under 70 Click the icon to view the number of politicians in each age bracket. a. Use the table and the $f / N$ rule to find $P(S)$. $P(S)=$ $\square$ (Type an integer or a decimal. Round to three decimal places as needed.) Number of Politicians Per Age Bracket \begin{tabular}{|lc|} \hline Age $(\mathbf{y r})$ & No. of politicians \\ Under 50 & 11 \\ $50-59$ & 29 \\ $60-69$ & 42 \\ $70-79$ & 19 \\ 80 and over & 3 \\ \hline \end{tabular} Print Done ining: 00:34:54 Submit test
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Solution

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Solution Steps

Step 1: Calculate Total Number of Politicians

The total number of politicians is calculated by summing the number of politicians in each age bracket:

\[ N = 11 + 29 + 42 + 19 + 3 = 104 \]

Step 2: Calculate Number of Politicians Under 70

The number of politicians under 70 is the sum of those under 50, in their 50s, and in their 60s:

\[ \text{Under 70} = 11 + 29 + 42 = 82 \]

Step 3: Calculate Probability \( P(S) \)

The probability \( P(S) \) of selecting a politician under 70 is given by the ratio of the number of politicians under 70 to the total number of politicians:

\[ P(S) = \frac{\text{Under 70}}{N} = \frac{82}{104} \approx 0.7885 \]

Rounding to three decimal places, we have:

\[ P(S) \approx 0.788 \]

Final Answer

\(\boxed{P(S) = 0.788}\)

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