Question

An integer is chosen at random from the first 200 positive integers. Find the probability thatit is divisible by 6 or 8.

Answer 1

Integers which are divisible by 6 only
= 200 / 6
= 33 2/6
Take round off value 33

Integers which are divisible by 8 only
= 200 / 8
= 25

LCM. Of 6 & 8 = 24 (numbers divisible by both 6 & 8)
Integers divisible by 24
200 / 24
= 8 8/24
Take round off = 8

Now p(E) = (33 + 25 - 8) / 200
= 50 / 200
= 1 / 4

Answer 2

Probability is 1 / 4

Step-by-step explanation:

Sample Space:

Integers that are divisible by 6:

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198.

Integers that are divisible by 8:

8,16,24,32,40,48,56,64,72,80,88,96,104,112.120,128,136,144,152,160,168,176,184,192,200.

Total no of common multiples of 6 and 8 till the first 200 positive integers:

=> 50

Total no of positive integers =  200

Probability of an Event P(E) :

$\fbox{P(E) = No Of Outcomes/Total No Of Outcomes }$

Probability that an Integer chosen at random from the first 200 positive integer is divisible by 6 or 8:

=> 50 / 200

=> 1 / 4

Therefore, the probability of choosing a random integer that is divisible by 6 or 8 is 1/4.