A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that (i) both the tickets have prime numbers on them (ii) on one there is a prime number and on the other, there is a multiple of 4.
given: bag containing tickets numbered 1-20
formula:
two tickets are drawn at random, total possible outcomes are 20C2
therefore n(S)=20C2=190
(i) let E be the event that both tickets have prime number
E= {2,3,5,7,11,13,17,19}
n(E)= 8C2=28
(ii) let E be the event that one ticket has prime number and other is a multiple of 4
E= {2,3,5,7,11,13,17,19} for prime number
E= {4,8,12,16,20} for multiple of 4
n(E)= 8C15C1=40