Question 946282
  
Given
Urn contains 7 red, 5 blue and 3 white marbles for a total of 15.
Three are drawn without replacement.
Find expected number of marbles drawn.
  
Solution
First we will need to find the probabilities of drawing 0, 1, 2 and 3 marbles.
P(0) = {{{8/15*7/14*6/13 = 8/65 }}}
P(1) = {{{3*(7/15*8/14*7/13) = 28/65 )}}}
P(2) = {{{3*(7/15*6/14*8/13) = 24/65 }}}
P(3) = {{{7/15*6/14*5/13 = 5/65 }}}
Check: P(0)+P(1)+P(2)+P(3) = 1, checks.
  
Next we will calculate the expected value of X = number of reds.
E[X] = Σ x*P(x) = {{{0*(8/65)+1*(28/65)+2*(24/65)+3*(5/65) = 7/5 = 1.4}}}
  
  
Answer
The expected number of red marbles drawn is 1.4