Asked by F0reveryoung
An urn has fifteen red balls and nineteen white balls. Three balls are selected at random and the number of red balls are observed.
Find the probability distribution for
Number of Red Balls:
0 =
1 =
2 =
3 =
Find the probability distribution for
Number of Red Balls:
0 =
1 =
2 =
3 =
Answers
Answered by
Priscilla
total amount of balls = 15 red + 19 white = 34 balls
0 - 0/34 = 0
1 - 1/34
2 - 2/34 = 1/17
3 - 3/34
0 - 0/34 = 0
1 - 1/34
2 - 2/34 = 1/17
3 - 3/34
Answered by
Reiny
Prob red = 15/34
prob white = 19/34
when picking three:
prob(0 red) = C(3,0) (19/34)(18/33)(17/32) = 57/352
prob(1 red) = C(3,1) (15/34)(19/33)(18/32) = 2565/5984
prob(2red) = C(3,2) (15/34)(14/33)(19/32) = 1998/5984
prob (3red) = C(3,3)(15/34)(14/33)(13/32) = 455/5984
notice that the sum of the 4 fractions above is 5984/5984 = 1
prob white = 19/34
when picking three:
prob(0 red) = C(3,0) (19/34)(18/33)(17/32) = 57/352
prob(1 red) = C(3,1) (15/34)(19/33)(18/32) = 2565/5984
prob(2red) = C(3,2) (15/34)(14/33)(19/32) = 1998/5984
prob (3red) = C(3,3)(15/34)(14/33)(13/32) = 455/5984
notice that the sum of the 4 fractions above is 5984/5984 = 1
Answered by
Reiny
the 2nd last prob calculation should be 1995/5984
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