Question

(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8.

Answer 1

3 red 5 green s totcel For First step, nai P(red) = 36 For n = 2 (second step) let comsider no. of red ball after Rstel, mo.of red balva (8+) No.of greembal} = (8+) :. For n=ktl, Total number of red balus - (3)*(8+x+2) +(*)(*)(8+R) EL (90+ 9 + 120+158) PE = 3, PSRS + 0.375 R Therefore, No. of green ball) = (8+X+))- (no. of zed ball) = (8+*+1)-( 3.28125 +0.375 k) = 0.625 X +5.71875 .: Pcred) = 3.28125+ 0.375 R g+k 0.375 35 stillsame. Przed) = CS Scanned with CamScanner