Probability 17013

What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number?

Correct answer:

p =  0.3375

Step-by-step explanation:

$$\begin{gathered} x_1=22;\frac{22}{11} \\ {x}_2=23;P \\ {x}_3=27;3^3=27 \\ {x}_4=29;P \\ {x}_5=31;P \\ {x}_6=33;\frac{33}{11} \\ {x}_7=37;P \\ {x}_8=41;P \\ {x}_9=43;P \\ {x}_{10}=44;\frac{44}{11} \\ {x}_{11}=47;P \\ {x}_{12}=53;P \\ {x}_{13}=55;\frac{55}{11} \\ {x}_{14}=59;P \\ {x}_{15}=61;P \\ {x}_{16}=64;4^3=64 \\ {x}_{17}=66;\frac{66}{11} \\ {x}_{18}=67;P \\ {x}_{19}=71;P \\ {x}_{20}=73;P \\ {x}_{21}=77;\frac{77}{11} \\ {x}_{22}=79;P \\ {x}_{23}=83;P \\ {x}_{24}=88;\frac{88}{11} \\ {x}_{25}=89;P \\ {x}_{26}=97;P \\ {x}_{27}=99;\frac{99}{11} \\ p=\frac{27}{80}=0.3375 \end{gathered}$$

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