A box contain 100 cards marked with numbers 1 to 100. If one card is drawn from the box, find the probability that it bears (i) single digit number, (ii) two-digit numbers (iii) three-digit number (iv) a number divisible by 8 (v) a multiple of 9, (vi) a multiple of 5.

Given, total number of cards in the box is 100 with each card marked with numbers from 1 to 100.

Therefore, we know that from 1 to 100 , number of single digit numbers = 1 to 9 = 9

Also, number of two-digit numbers from 1 to 100 = 10 to 99 = 90

Only three digit number from 1 to 100 is 100.

So, number of three-digit numbers from 1 to 100 = 1

Numbers divisible by 8 from 1 to 100 are 8,16,24,32,40,48,56,64,72,80,88,96 = 12

Numbers which are multiple of 9 are 9,18,27,36,45,54,63,72,81,90,99 = 11

Numbers which are multiple of 5 are 5,10,15,20,……….100 = 20

Now, let the event that a single digit number is drawn from the box be A.

Event that card bearing a two-digit number is drawn from the box be B.

Event that a card bearing a three-digit number is drawn from the box be C.

Event that a card bearing a number divisible by 8 is drawn from the box be D.

Event that a card bearing a number which is multiple of 9 is drawn from the box be E.

Event that a card bearing a number which is multiple of 5 is drawn from the box be F

Number of favourable outcomes of event A = 9

Number of favourable outcomes of event B = 90

Number of favourable outcomes of event C = 1

Number of favourable outcomes of event D = 12

Number of favourable outcomes of event E = 11

Number of favourable outcomes of event F = 20

Total number of favourable outcomes = 100

(i) Probability of the card bearing a single digit number = Probability of occurrence of event A = P(A)

P(A) = 0.09

(ii) Probability of the card bearing a two-digit number = Probability of occurrence of event B = P(B)

P(B) = 0.9

(iii) Probability of the card bearing a three-digit number = Probability of occurrence of event C = P(C)

P(C) = 0.01

(iv) Probability of the card bearing a number divisible by 8 = Probability of occurrence of event D = P(D)

P(D) = 0.12

(v) Probability of the card bearing a number which is multiple 9 = Probability of occurrence of event E = P(E)

P(E) = 0.11

(vi) Probability of the card bearing a number which is multiple 5 = Probability of occurrence of event F = P(F)

P(F) = 0.2