A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to b

Question

A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to be selected, then probability distribution of X is given by

Quantrex Academy · Accepted Answer

Correct answer: 0

X denote the number of times black ball is drawn. Since a ball is drawn three times, 0,1,2 and 3 are possible values of X . Probability of getting a black ball in a single draw from bag is p = 3 7 and q =1- 3 7 = 4 7 aligned & P [ X =0]= P [ no black ball ]= qqq = q ^3= ( 4 7 )^3 & P [ X =1]= P [ one black ball ] &= pqq + qpq + qqp &=3 pq ^2 &=3 ( 3 7 ) ( 4 7 )^2= 9 7 ( 4 7 )^2 & aligned P [ X =2] & = P [ two black balls ] & = ppq + pqp + qpp & =3 p ^2 q =3 ( 3 7 )^2 ( 4 7 )= 12 7 ( 3 7 )^2 aligned aligned P [ X =3

A bag contains 4 red and 3 black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let X denote the number of times black ball is drawn in 3 draws. Assuming that at each draw each ball is equally likely to be selected, then probability distribution of X is given by

Correct answer

Step-by-step solution

More from Probability