Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 19
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Answers
11.
10
The probability of at least one defective in a batch is 1
0.9
= 0.6513.
Let the probability of at least one defective in exactly j batches be p .
7
10 4
10 3
4
3
(a)
p
=
1
0.9
0.9
= 35
0.6513
0.3487
= 0.2670.
4
4
(b)
7
10 5
10 2
5
2
p
=
1
0.9
0.9
= 21
0.6513
0.3487
= 0.2993.
5
5
7
10 6
10 1
6
1
p
=
1
0.9
0.9
= 7
0.6513
0.3487
= 0.1863.
6
6
7
10 7
10 0
7
p
=
1
0.9
0.9
= 0.6513
= 0.0497.
7
7
The probability of at least one defective in four or more of the batches is
p
+ p
+ p
+ p
= 0.8023.
4
5
6
7
12.
(a) Let Y be the number of companies to which the engineer is called and let A denote the event
that the engineer is called to company A.
4
(i) P(Y = 4) = 0.1
= 0.0001.
4
3
1
4
(ii) P(Y
3) =
0.1
0.9
+ 0.1
= 0.0037.
3
P(Y = 4
Y
1)
(iii) P(Y = 4 Y
1) =
P(Y
1)
P(Y = 4)
0.0001
0.0001
1
=
=
=
=
= 0.0003.
4
P(Y
1)
1
0.9
0.3439
3439
P(Y = 4
A)
(iv) P(Y = 4 A) =
P(A)
P(Y = 4)
0.0001
=
= 0.0010.
P(A)
0.1
(b) The mean is E(Y ) = 4
0.1 = 0.4. The variance is V (Y ) = 4
0.1
0.9 = 0.36.
35
HELM (2008):
Section 37.2: The Binomial Distribution
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