A box contains the following numbered tickets 11599 a If I d

A box contains the following numbered tickets: 1,1,5,9,9

a) If I draw two tickets with replacement, what is the chance that the sum of the two tickets is greather than or equal to 10?

b) If I repeat the procedure in a) 8 times (i.e. draw 2 tickets and find their sum, and do this 8 times), what is the chance that I get a sum greater than or equal to 10 exactly 6 of the 8 times?

Solution

a ) if with replacement is done the exp then the total sample space will be 25

and the sum bigger then 10 0r equal to will be = 12

probability = 12/25

b) 8 times the exp is done

probability of equal or more then 10 = 12/25

probability less then 10 = 13/25

p(x=6) = 8C6(12/25)^6*(13/25)^2 = 0.092