Problem Code: 210609MATH

[Amit Goyal]

Suppose that a box contains one fair coin and one coin with a head on each side. Suppose that a coin is selected at random and that when it is tossed three times, a head is obtained three times. Determine the probability that the coin is the fair coin.

[nidhi]

ans. 1/9

[nidhi]

 sorry..same question had already been replied . i didnt notice

[Amit Goyal]

perfect

[PRANAVjain]

HOW THE PROBABILITY COMES OUT TO BE 1/9?
P(F/3 HEADS)=P(F n 3 HEADS)/P(3 HEADS)
{n MEANS INTERSECTION}

IS THIS THE WAY TO SOLVE IT?

[duck]

hi pranav, it can be solved in the following way>>

let, Fair coin be "F"
unfair coin be "U"
and 3 heads be "3H"

P(F)=1/2 , P(U)=1/2

P(3H/f)=1/2 * 1/2 * 1/2 = 1/8

P(3h/U)=1*1*1= 1

NOW,
P(F/3H)= P(3H/F)* P(F)
            --------------
             P(3H/F)* P(F) + P(3H/U)* P(U)

           =     (1/8* 1/2)
             ---------------
            (1/8*1/2)+ (1*1/2)

          =1/9

[Amit Goyal]

Perfect answer Nidhi

[duck]

Thanku Sir :)

[PRANAV JAIN]

THANX NIDHI...MAY I KNOW FROM WHICH COLLEGE U R and wat u r doing?I THINK U CAN HELP ME A LOOOOTTTT...SERIOUSLY AND I NEED UR HELP TOO...THOU ITS BEING MY SELFISH MOTIVE HERE(lol) BUT STILL I THINK U WONT SAY no...
reply me soon...waiting...

[priyanka p]

a price taking firm makes machine tools Y using labor and capital according to the production function Y=K^0.25 L^0.25.  Labor can be hired at the beggining of every week while capital can be only hired at the beggining of every month. 1 onth is long period and 1 week is short period.the wage rate per week and rental rate of capital per month are both 10. given info, find short run and long run cost functions of firm. 2nd part-- what is the long run profit maximising no. of machine tools? how many units of labor and capital should the firm hire at the beginning of january?

[Amit Goyal]

Assuming one month has 4 weeks:
Short-run Cost function(w, r, K, Y) = w(Y^4)/(K)  + (rK)/4
Given that w = r = 10, Short-run Cost function(K, Y) = 10((Y^4)/(K)  + K/4)
Notice that rental rate of capital(r) is 10 per month and wage rate(w) is 10 per week.
Long-run Cost function(w, r, Y)* = 2((w(r/4))^0.5)(Y^2) = ((wr)^0.5)(Y^2)
*This is long run cost per week.
Given that w = r = 10, Long-run Cost function(Y) = 10(Y^2)
Profit maximizing no. of machine tools produced in a week = (p/20) where p is the per-unit price of machine tools
No. of labor units = (p^2)/(800)
No. of capital units = (p^2)/(200)

[priyanka p]

thank you sir

[priyanka p]

but sir i didnt understand the long run funcyion, why we took 2 in the beggning