Suppose a bag has 11 balls with 5 red and 6 green Draw 4 bal

Suppose a bag has 11 balls, with 5 red and 6 green. Draw 4 balls with replacement and let X be the number of red balls you draw. Compute the probability mass function p(x) of X. Use a calculator to find the decimal approximations. Now find the expected number of red balls by computing E{X) using a calculator and the formula Did you get a decimal close to 4 .5/11?

Solution

Given that bag has 11 balls, with 5 Red balls and 6 Green
Drawing a 4 balls with replacement
   \'0\' Red balls = All are Green = (6/11)^4 = 0.088518
   \'1\' Red balls = 1 Red, 3 Green = 5/11 * (6/11)^3 = 0.07376
   \'2\' Red balls = 2 Red, 2 Green = (5/11)^2 * (6/11)^2 = 0.06147
   \'3\' Red balls = 3 Red, 1 Green = (5/11)^3 * (6/11)^1 = 0.0512
   \'4\' Red balls = 4 Red = (5/11)^4 = 0.042688

Calculation of MEAN

f=   0.317636
fx =   0.521052
  
Mean = fx / f =   1.6404

Values ( X )	Frequency(f)	fx	( X^2)	f x^2
0	0.088518	0	0	0
1	0.07376	0.0738	1	0.0738
2	0.06147	0.1229	4	0.2459
3	0.0512	0.1536	9	0.4608
4	0.042688	0.1708	16	0.683