SOLUTION: A bag has 7 balls: a green, black, blue, brown, pink, red, and orange one. If 6 balls are removed from the bag at random, what is the probability that a blue ball has been removed?

Question 983386: A bag has 7 balls: a green, black, blue, brown, pink, red, and orange one. If 6 balls are removed from the bag at random, what is the probability that a blue ball has been removed?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's say we had 6 slots A through F

7 choices for slot A
6 choices for slot B
5 choices for slot C
4 choices for slot D
3 choices for slot E
2 choices for slot F

7*6*5*4*3*2 = 5040

If order mattered, then there would be 5040 ways to pick the six balls. However, order doesn't matter so we divide by 6! = 720 to get 5040/720 = 7

There are 7 ways to pick the six balls (out of a pool of 7), where again, order doesn't matter.

-----------------

If we reserve a slot, say slot A, for a blue ball, then there are 5 slots left and 6 items to fill those slots.

Using the same idea above, we can take a shortcut using the combination formula to say 6 C 5 = 6

There are 6 ways to pick a set of balls where one is definitely blue.

This is out of 7 ways total to pick the balls (we don't care if we get blue or not here)

That's why the answer is 6/7
=======================================================

Alternative Method:

Think of it in a reverse way. Think of it as "what is the probability of blue NOT being chosen?". In other words, "what is the probability of blue being left in the bag?"

Well that's simply 1/7. There is a 1 in 7 chance of picking blue, so there is a 1/7 chance that blue remains in the bag.

That means there is a chance that blue is not in the bag.

=======================================================

Either way, the final answer is 6/7
RELATED QUESTIONS
A bag contains two black balls three green balls and four red balls. a ball is pick from... (answered by solver91311)

If five balls are drawn from a bag containing six green balls, eight blue balls, and ten... (answered by Boreal)

A bag contains two black balls three green balls and four red balls. a ball is pick from... (answered by solver91311)

If 3 balls are drawn at random from a bag containing 3 red and 4 blue balls, what is the... (answered by stanbon)

A bag contains blue,red and orange balls. There are 3 times as many blue balls as there... (answered by Boreal)

A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without... (answered by ikleyn,greenestamps)

A bag contains 7 white 5 black and 4 red balls. If 2 balls are drawn at random. What is (answered by Fombitz)

One bag contains 5 blue balls and 4 green balls. A second bag contains 2 blue balls and 5 (answered by Boreal)

A bag contains three black balls,four white balls and five red balls.Three balls are... (answered by ikleyn)