Posted by **Sharon** on Tuesday, October 6, 2009 at 11:57am.

A box contains 4 red and 3 blue poker chips. What is the probability when 3 are selected randomly that all 3 wil be red if we select chips with replacement?

a.) Without replacement?

- probability -
**MathMate**, Tuesday, October 6, 2009 at 4:08pm
To get one red out of the seven, you have 4 chances, so the probability is

4/7.

Since the chips will be replaced, the second and subsequent draws will be under the same conditions, i.e. they are independent. The probability of each subsequent draw is again 4/7.

The probability of joint independent events is the product of the individual probabilities, thus

in this case,

(4/7)*(4/7)*(4/7)=?

Without replacement, after each successful draw, there will be one red chip less.

Probability for first draw:

4/7 as before

second draw:

3/6

third draw:

2/5

So probability of all three events happening:

(4/7)*(3/6)*(2/5)

=4/35

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