SOLUTION: Please help me solve this problem : the numbers 1,2,...,10 are written on ten cards and placed in a hat. cards are then draw one by one without replacement. find the probabilit

Question 238007: Please help me solve this problem :

the numbers 1,2,...,10 are written on ten cards and placed in a hat. cards are then draw one by one without replacement. find the probabilities of the following events:
A: exactly three even numbers are obtained in the first five draws;
B: exactly five draws are requied to get three even numbers; i.e. there are two even numbers in the first four draws, followed by an even number on the fifth draw;
C: number 7 occurs on the 4th draw;
D: the largest number obtained in the first three draws is 5.

and thank you in advance
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
nCr=n!/((n-r)!r!) Combination of n things taken r at a time.
.
A)( 5C3 * 5C2)/10C5 = 10*10/252=.397
.
B) ((5C2 * 5C2)/10C4) * 1/2 = (10*10)/210 * 1/2 =.238
.
C) 1/10 if no cards have been drawn yet.
.
D) 5C3 / 10C3 = 10/120 = 1/12
.
Ed
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