Ams 310 Survey Of Probability And Statistics Worksheet - Midterm Exam I - Stony Brook University Page 10
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11(8). (a). There are 6 white balls and 10 black balls in a bag. If a person randomly draws
4 balls from the bag, what is the probability that two balls are black?
(b). If the person put the ball back to the bag after each draw, what is the proba-
bility that in 4 draws, two are black?
(c). If the ratio of white and black balls is kept at 6/10, as the total number of
balls in the bag increases, what is the best way to calculate the approximate
probability of (a)?
Solution:
(a). This is hypergeometric probability distribution problem with
,
N = 16
a = 10
and
n = 4
10
6
2
2
P (x = 2) = G(x = 2; 40, 6, 4) =
40
4
(b). This is a binomial probability distribution problem with
and
n = 4
p = 10/16 =
0.625
4
2
2
P (x = 2) = B(2; 4, 0.625) =
0.625
0.375
2
(c). When
is very large and
remain unchanged, the hypergeometric distri-
N
a/N
bution can be approximated by the binomial distribution, therefore
P (x = 2)
B(2; 4, 0.625)
should be used because the calculation is much easier.
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