Question

To win a prize in a competition a door number in an apartment block is chosen at random from the numbers 1 to 150. Find the probability that the door number is:A square numberAt least 100 Divisible by 5No more than 11.

Answer 1

Step-by-step 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

`Pr(E)=\frac{\text{number of favourable outcomes}}{Total\text{ number of possible outcomes}}`

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

`Pr(\text{square number) = }\frac{\text{12}}{150}=(2)/(25)`

Answer:

`(2)/(25)`

Part B

At least 100 implies from 100 to 150. This gives 51 favorable numbers.

`Pr(At\text{ least a 100)=}\frac{\text{51}}{150}=(17)/(50)`

Answer:

`(17)/(50)`

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.

`Pr(\text{Divisible by 5) = }\frac{\text{30}}{150}=(1)/(5)`

Answer:

`(1)/(5)`

Part D

The numbers no more than 11 are 11 favorable numbers

`Pr(No\text{ more than 11) =}\frac{\text{11}}{150}`

Answer:

`(11)/(150)`