The probability of taking a step forward by a man is 1/2. Calculate the probability that he has moved 4 steps forward in 10 steps.
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Answer:
As 0.4+0.6=1, the man either takes a step forward or a step backward. Let a step forward be a success and a step backward be a failure.
Then, the probability of success in one step
=p=0.4=
5
2
The probability of failure in one step =q=0.6=
5
3
.
In 11 steps he will be one step away from the staring point if the numbers of successes and failure differ by 1.
So, the number of successes =6
The number of failures =5
or the number of successes =5,
The number of failures =6
∴ the required probability =
11
C
6
p
6
q
5
+
11
C
5
p
5
q
6
=
11
C
6
(
5
2
)
6
.(
5
3
)
5
+
11
C
5
(
5
2
)
5
.(
5
3
)
6
=
6!5!
11!
.(
5
2
)
5
.(
5
3
)
5
.{
5
2
+
5
3
}
=
120
11.10.9.8.7
.
5
10
2
5
.3
5
=462×(
25
6
)
5
.
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