Let S 1 2 3 12 an equiprobable sample space Let A be th

Let S = {1, 2, 3, . . . , 12}, an equiprobable sample space. Let A be the event of selecting a number less than or equal to 6, and let B be the event of selecting a number that is a multiple of 3. Determine whether A, B are independent.

Solution

Solution:

S = {1, 2, 3, . . . , 12}

Let A be the event of selecting a number less than or equal to 6

A = {1, 2, 3,4,5,6},

Probablity(A)=favourable cases/total outcomes= 6/12=1/2=0.5

let B be the event of selecting a number that is a multiple of 3.

B={3,6,9,12}

Probability of B=P(B)=4/12 =1/3

there are 2 nos common between A and B

P(AB)=2/12=1/6

Two events are independent if, and only if, P(A B) = P(A) * P(B)

LHS=P(A)P(B)=(1/2)*(1/3)=1/6

RHS= P(AB)=1/6

LHS=RHS

Therefore A, B are independent