Q. 135.0( 3 Votes )

A number is chosen from the numbers 1 to 100. Find the probability of its being divisible by 4 or 6.

Answer :

let A denote the event that the number is divisible by 4 and B denote the event that the number is divisible by 4.


To find : Probability that the number is both divisible by 4 or 6 = P(A or B)


The formula used : Probability =


P(A or B) = P(A) + P(B) - P(A and B)


Numbers from 1 to 100 divisible by 4 are 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100.


There are 25 numbers from 1 to 100 divisible by 4


Favourable number of outcomes = 25


Total number of outcomes = 100 as there are 100 numbers from 1 to 100


P(A) =


Numbers from 1 to 100 divisible by 6 are


6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96


There are 16 numbers from 1 to 100 divisible by 6


Favourable number of outcomes = 16


Total number of outcomes = 100 as there are 100 numbers from 1 to 100


P(B) =


Numbers from 1 to 100 divisible by both 4 and 6 are


12,24,36,48,60,72,84,96


There are 8 numbers from 1 to 100 divisible by both 4 and 6


Favourable number of outcomes = 8


P(A and B) =


P(A or B) = P(A) + P(B) - P(A and B)


P(A or B) =


P(A or B) =


P(A or B)


The probability that the number is both divisible by 4 or 6 = P(A or B)


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