Probability Distribution

Find the Probability Distribution for the number of Jazz Records, when 4 Records are selected at random from collection consisting of 5 Jazz Records, 2 Classical Records and 3 Polka Records. Find the expected number.

If 4 are selected from 5 Jazz, all will be Jazz. What is your question? P. D. of classical records or P. D. of Polka?


P.D. of the number of Jazz records..

Let X be the number of jazz records selected. Then, distribution of X is
X = x:-- -- ---0---- ----- ----- -----1---- --- --- --- --2---- --- --- ------3--- --- -- --- -- --4-- -- --- -
p(x) :-5c0*5c4/10c4--5c1*5c3/10c4--5c2*5c2/10…
p(x) :-- --- ---5/210--- ----- ---50/210---- --- ---100/210- -- ----50/210--- ---- --5/210- -- --

E(X) = 420/210 = 2

Easy method:
Let X1, X2, X3 and X4 be the jazz in the 1st, 2nd, 3rd and 4th draws.
Then, E(Xi) = 0.5.
E(X) = E(X1) + E(X2) + E(X3) +E(X4) = 2

Good luck

Hi! I'll try to help you here. First we can observe that we have 10 records total. If 4 records are selected at random that means we have a 4/10 chance. since there are 5 jazz records we have a 5/10 chance of getting a jazz record. simple multiply 4/10 with 5/10. The result will get you 1/5. This means that you have a 1/5 probability of selecting a jazz record. We need to do the same thing with the other records. there are 2 classical records and 10 records total. Therefore the chance of getting a classical record would be 2/10. 2/10 x 4/10= 2/25. So we have a 2/25 chance of getting a classical record. Now finally we have 3 polka records left. Do the same thing. 3/10 x 4/10 = 3/25. Now we have a 3/25 chance of getting a polka record. It might seem confusing but if you ponder a bit you will get it.

WellThe prob of selecting 4 Jazz records is 1. That's it!