11.9% of a population is 65 or older.
That is;
[tex]\begin{gathered} P(65\text{ or older) = 0.119} \\ P(\text{younger than 65) = 0.881} \end{gathered}[/tex]
The probability of at most 2 is;
[tex]\begin{gathered} P(at\text{ most 2)=P(none) + P( one is older) + (two are older)} \\ P(none)=^{25}C_0(0.119)^0(0.881)^{25} \\ P(none)=1(1)(0.0421) \\ P(none)=0.0421 \end{gathered}[/tex][tex]\begin{gathered} P(1)=^{25}C_1(0.119)^1(0.881)^{24} \\ P(1)=25(0.119)(0.0478) \\ P(1)=0.1422 \\ P(2)=^{25}C_2(0.119)^2(0.881)^{23} \\ P(2)=300(0.119)^2(0.881)^{23} \\ P(2)=0.2305 \end{gathered}[/tex][tex]\begin{gathered} P(at\text{ most 2)=0.0421+0.1422+0.2305} \\ P(at\text{ most 2)=}0.4148 \end{gathered}[/tex]
The probability that at most 2 are 65 or older is 0.415 (round to three decimal places)
