ezinis wrote:

A bag contains 5 yellow balls and 6 orange balls.

Bag of 11 choices.

ezinis wrote:

When 4 balls are drawn at random simultaneously from the bag,

Combo box arrangement

(_)(_)(_)(_)/4!

ezinis wrote:

what is the probability that not all of the balls drawn are orange?

Probability Table. Create and work backwards.

# of Oranges: Events

0:

1:

2:

3:

4:

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

Total =

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Total = 11 pick 4 = 11C4 = 11*10*9*8/4*3*2*1 = 330

Orange = 4: 6 orange pick 4 = 6C4 = 6*5*4*3/4*3*2 = 15 <----------- at this point the question can be answered, but I'll continue filling in the table for fun.

Orange = 3: 6 orange pick 3 AND 5 yellow pick 1 = 6C3 * 5C1 = 100

Orange = 2: 6 orange pick 2 AND 5 yellow pick 2 = 6C2 * 5C2 = 150

Orange = 1: 6 orange pick 1 AND 5 yellow pick 3 = 6C1 * 5C3 = 60

Orange = 0: 5 yellow pick 4 = 5C4 = 5

OR Sum the table total: 330 - (15+100+150+60) = 5

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# of Oranges: Events

0: 5

1: 60

2: 150

3: 100

4: 15

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

Total = 330

****************************************************

Use the info in the table to answer any probability question.

P(Orange = 0) = 5/330

P(Orange = 1) = 60/330

P(Orange = 2) = 150/330

P(Orange = 3) = 100/330

P(Orange = 4) = 15/330

P(Orange <> 4) = P(Orange = 0,1,2,or3) = (5+60+150+100)/330 = 1 - 15/330 = 21/22

P(Orange = Odd) = (60+100)/330