Math, asked by rishilaugh, 1 year ago

Find the probability that a number from 1 to 300 is divisible by 3 or 7 ?

Answers

Answered by kvnmurty
3
Total number of  integer numbers  given:  300
Let  X be a number randomly chosen from 1 to 300.

Numbers divisible by 3:   3 * 1, 3 * 2, ..... 3 * 100 :   so there are 100 of them.

Numbers divisible by 7:   7 * 1, 7*2, .... 7*42 = 294   
so there are  42 of them.

Numbers divisible by both 3 and 7: ie, by 21:  21*1, 21*2, ... 21*14=294
so there are 14 of them.

Now we have totally 100 + 42 - 14 = 128 integers from 1 to 300 which are divisible by 3 or 7.

Probability = 128 / 300 = 32/75


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Answered by Anonymous
1
total numbers divisible my 3 is 3,6,9,...,300

n = 300/3 = 100

total numbers divisible by 7

7,14,21,..., 294

294 = 7 + (n1-1)7

n1 = 42

numbers divisible by both 3 and 7
21,42,63,...,294

n2= 294/21 = 14

by principle of exclusion theory

total numbers = 100 + 42 - 14 = 128

probability = 128/300 = 32/75
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