Question

Urn A contains two red balls and eight blue balls. Urn B contains two red balls and ten green balls. Six balls are drawn from urn A and four are drawn from urn B; in each case, each ball is replaced before the next one is drawn. What is the most likely number of blue balls to be drawn? What is the most likely number of green balls to be drawn?

Answer 1

TOPIC:Use of the Binomial distribution.

To answee the given mestion at diost we will move the jollouing as- X Bin (n, h)then E (x) Proo! X Bin -x tud P=) 2) G-)-; X91,2 ; elbewhere E (x). P (x ). %. 2 ="Mnp- = np. TProvedy 1

Dline, X,= No. b we balls dnawn dnawn tnom unn (with nepu placement Then, Xi Bin (m6, P, [ AJ, to tal 6 balls we dnaw and there are total & blue balis out balls -10 upn A (x) . E 6X0.8. = 4.8 Simiterty detine, X No. graen balls drawn (with nom unn B meplacemeu Then X NBin 12 We dnaw 4 balus dram unn B and there are 10 green balls in unn B ut the total 12 baus 3.3333

we dind, E (x) 4. 8 most like y blue balls to be dmawn is 5. numben So, the of balls dnawn, should as, no. be an 4painy (x2)=3.3333 green 3. Lo, the most Nhey numb er balls to be drsawn io ( as, no. balls drawn, s hould be [iruurea