The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year?

• There are 6 winning funds that grew more than 10%, and 4 losing funds that grew less than 10%.The problem can be split into 3 sub-problems:
  
  1)Sam has to choose 3 winning funds.
  This can be done in 6C3 ways.
  
  2)Sam has to choose 1 losing fund.
  This can be done in 4C1 ways.
  
  Or
  3)Sam has to choose all 4 funds to be winning funds.
  This can be done in 6C4 ways.
  
  This is how Sam chooses at least 3 winning funds.Hence, the total number of ways of choosing at least 3 winning funds is 6C3 x 4C1 + 6C4.
  
  If there were no restrictions (such as choosing at least 3 winning funds), Sam would have chosen funds in 10C4 ways.
  
  Hence, the probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year is
  
  (6C3 x 4C1 + 6C4)/10C4
• 12 years agoHelpfull: Yes(16) No(2)
• The probability that at least 3 of Sam’s 4 funds grew by at least 10% over the last year is ----> (6C3 x 4C1 + 6C4)/10C4
• 12 years agoHelpfull: Yes(2) No(2)