Binominal Distributions Worksheet With Answer Key - Helm 2008 Section 372 Page 10
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20Task
1
Using the binomial model, and assuming that a success occurs with probability
5
in each trial, find the probability that in 6 trials there are
(a) 0 successes
(b) 3 successes (c) 2 failures.
Let X be the number of successes in 6 independent trials.
Your solution
(a) P(X = 0) =
Answer
1
4
In each case p =
and q = 1
p =
.
5
5
Here r = 0 and
6
4
4096
6
P(X = 0) = q
=
=
0.262
5
15625
Your solution
(b) P(X = 3) =
Answer
3
3
6
5
4
1
4
20
64
12
80
6
3
3
r = 3 and
P(X = 3) =
C
p
q
=
=
=
= 0.0819
3
6
1
2
3
5
5
5
15625
Your solution
(c) P(X = 4) =
Answer
4
2
2
6
5
1
4
15
4
240
6
4
2
Here r = 4 and P(X = 4) =
C
p
q
=
=
=
= 0.01536
4
6
1
2
5
5
5
15625
26
HELM (2008):
Workbook 37: Discrete Probability Distributions
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