# probability

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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 -

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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