SOLUTION: Consider an experiment of drawing 4 cards at random from a bag containing 7 cards marked with integers from 1 to 7. - Find the sample space S1 of the experiment if the first car

Click here to see ALL problems on Probability-and-statistics

Question 1147313: Consider an experiment of drawing 4 cards at random from a bag containing 7 cards marked with integers from 1 to 7.
- Find the sample space S1 of the experiment if the first card is replaced before the second.
- Find the sample space S2 of the experiment if the first card is not replaced.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

(1) The definition of the two problems is not clear. The difference between the two cases is that in one case the first card is replaced before drawing the second, and in the other case it is not. But the problem says nothing about whether the second card is replaced before drawing the third, or whether the third card is replaced before drawing the fourth. The answers will of course be different, depending on the answers to those questions.

(2) Regardless of the correct interpretation of the problem, the sample space is large; it will be tedious to write it all out. We aren't going to spend our time doing that for you; and you wouldn't learn anything by having us do it for you.

Answer by ikleyn(52816) (Show Source):
You can put this solution on YOUR website!
.

Case 1

In this case, the sample space is the set of all objects { (X, YZW) }, where X is any integer number between 1 and 7 inclusively and YZW is the triple of different (non-repeating) integer numbers from 1 to 7 inclusively, where X and Y can be equal OR UNEQUAL integer numbers (so, there is NO restrictions for equality or inequality of the values of X and Y in this sample set). The number of elements in this sample space is 7*(7*6*5) = 1470.

Case 2

In this case, the sample space is the set of all quadruples { XYZW } of non-repeating integer numbers X, Y, Z and W from 1 to 7, inclusively. The number of elements in this sample space is 7*6*5*4 = 840.