Question

The probability that a number selected at random between 100 and 999 (both inclusive) will not contain the digit 7 is:

Answer 1

10 numbers with first digit 7 (107, 117, ……, 197). 10 numbers with 7 in the second place (170, 171, ……, 179). The number 177 is common to both, and therefore gets counted twice — so subtract one. Hence 10+10 -1 = 19.

Count in the other centuries

200–299: 19 (Same logic)

300–399: 19 (Same logic again)

……

600–699: 19

700–799: 100 (Obviously)

800–899: 19 (Same logic as the 100–199 century)

900:999 : 19. (Ditto)

So totally, we have 8 ‘centuries’ with 19 numbers each containing at least one 7 each, and one ‘century’ with a 100 numbers containing the number 7, for a total of 19×8+100=25219×8+100=252.

So, numbers without the digit 7 ==900−252=648900−252=648.

So the probability of drawing a number without the digit 7 =648900=0.72.

Answer 2

probability is 0.72.......