Answer :
Explanation
From the question, the winning door number must be selected from 1 to 150.
Recall that the formula for the probability of an event is given as
[tex]Pr(E)=\frac{\text{number of favourable outcomes}}{Total\text{ number of possible outcomes}}[/tex]The total possible numbers is from 1 to 150 which gives 150 numbers. We can then find the favorable outcomes for each of the questions.
Part A
When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 are the square numbers from 1 to 150.
In total, we have 12 square numbers. Therefore, the probability is given as
[tex]Pr(\text{square number) = }\frac{\text{12}}{150}=\frac{2}{25}[/tex]Answer:
[tex]\frac{2}{25}[/tex]Part B
At least 100 implies from 100 to 150. This gives 51 favorable numbers.
[tex]Pr(At\text{ least a 100)=}\frac{\text{51}}{150}=\frac{17}{50}[/tex]Answer:
[tex]\frac{17}{50}[/tex]Part C
The numbers divisble by 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150. This gives a total of 30 favorable numbers.
[tex]Pr(\text{Divisible by 5) = }\frac{\text{30}}{150}=\frac{1}{5}[/tex]Answer:
[tex]\frac{1}{5}[/tex]Part D
The numbers no more than 11 are 11 favorable numbers
[tex]Pr(No\text{ more than 11) =}\frac{\text{11}}{150}[/tex]Answer:
[tex]\frac{11}{150}[/tex]