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




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