There are 6 chips in the box The chips are numbered 1 throug

There are 6 chips in the box. The chips are numbered 1 through 6: 1, 2, 3, 4, 5, 6.

You randomly take one chip from the box, record the number
and put the chip back to the box. Then you take another chip from the box,
record the number and put the chip back to the box.
Then repeat it one more times with third chip.

a) How many elements are in the sample space of this experiment?
Use the Fundamental Counting Rule to find number of possible outcomes.

b) What is the probability that all three chips will have different number?
Divide number of outcomes with all different numbers over total number of possible outcomes.

c) What is the probability that all three chips will have even numbers?
Divide number of outcomes with all even numbers over total number of possible outcomes.

Solution

A)

There are 6 possibilities for each draw.

Hence, there are 6*6*6 = 216 possibilities. [answer]

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b)

To get 3 different numbers, there are 6P3 = 120 ways.

Thus,

P(3 different) = 120/216 = 0.555555556 [answer]

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c)

There are 3 ways that each draw has even numbers.

Thus, there are 3*3*3 = 27 ways to get all even numbers.

Hence,

P(all even) = 27/216 = 0.125 [answer]