Discussion Forum

A box contains 20 identical balls of which 10 are blue and 10 are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn 4 th time on the 7 th draw is 

Answer:

Explanation:

Probability  of getting a blue ball at any draw  =p= $\frac{10}{20}=\frac{1}{2}$

 P[ getting a blue ball 4th time in 7 th draw ]=P[ getting 3 blue balls in 6 draw]Λ P[ a blue-ball in the 7th draw]

$=^{6}C_{3}\left(\frac{1}{2}\right)^{3}\left(\frac{1}{2}\right)^{3}.\frac{1}{2}$

 =  $\frac{6\times5\times4}{1\times2\times3}(\frac{1}{2})^{7}=20\times\frac{1}{32\times4}=\frac{5}{32}$