A bag contains 6 balls. If three balls are drawn at a time and all of them are found to be green, then the probability that exactly 5 of the balls in the bag are green is:

Step-by-step solution

Let A be the event we draw three green balls. Let B be the event that fine balls are green. Let E₁ be event that there are 3 green balls. E₂ be event that there are 4 green balls. E₃ be event that there are 5 green balls. E₄ be event that there are 6 green balls. aligned & P(A)=P ( A E₁ ) P (E₁ )+P ( A E₂ ) P (E₂ ) & +P ( A E₃ ) P (E₃ )+P ( A E₄ ) P (E₄ ) & = ^3 C₃ ^6 C₃ ( 1 2 )^6+ ^4 C₃ ^6 C₃ ( 1 2 )^6 & + ^5 C₃ ^6 C₃ ( 1 2 )^6+ ^6 C₃ ^6 C₃ ( 1 2 )^6 aligned Required probability P ( B A )= P ( A B ) P(B) P(A) alig