Probability and divisible by questions help please!!?
A.) Five counterfeit coins are mixed with nine authentic coins. If two coins are drawn at random, what is the probability that one coin is authentic and one is counterfeit?
B.) What is the sum of the integers between 1 and 300 that are divisible by 11, 13 or both?
qa
P[one authentic & one counterfeit]
= P[1st authentic & 2nd counterfeit] +P[1st counterfeit & 2nd authentic]
= [9/14][5/13] + [5/14][9/13] = 0.4945 or 49.45 %
qb
divisible by 11 : 11*1, 11*2,…. 11*13, ….11*26, 11*27
sum = 11*(1+2+….+27) = 11*27*28/2 = 4158
divisible by 13 : 13*1, 13*2,…. 13*11, …. 13*22,13*23
sum = 13*(1+2+…+23) = 13*23*24/2 = 3588
reqd. sum
= 4158 + 3588 - 143 - 286
(to eliminate double counting of 11*13 & 11*26/13*22)
= 7317
edit: bad day at office for initial calculation errors !