Latest AIEEE Aptitude Question SOLUTION: A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point

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(#M40017902) AIEEE Programming question probability Keep an EYE

A man takes a step forward with probability 0.4 and backward with
probability 0.6. Find the probability that at the end of eleven steps he is
one step away from the starting point

Asked In AIEEE jatin (11 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

Bankim  (11 years ago)

The man would be a step away from starting point in two cases:

1. He takes 6 steps forward and 5 steps backward
2. He takes 5 steps forward and 6 steps backward

For 1st case:
p1 = (11C6)(0.4)^6*(0.6)^5

for 2nd case:

p2 = 11C5(0.4)^5*(0.6)^6

total probability = p1 + p2 = 11C6 * (0.4)^6 * (0.6)^5 + 11C5 * (0.4)^5 * (0.6)^6
= 11C5 * (0.4)^5 * (0.6)^5 * (0.4 + 0.6) >>>>>>>(because 11C6 = 11C5)
= (11x10x9x8x7)/(1x2x3x4x5) * (0.24)^5
= 0.368.

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Samik Mukherjee  (11 years ago)

Since after 11 steps he is one away from the starting point, there are 2 ways this can happen:
a) He will take 5 steps forward and 6 steps backward
b) He will take 6 steps forward and 5 steps backward
There can be permutation in these two choices.

The probability for the 1st point: 0.4^5+0.6^6=0.01024+0.046656=0.057(approx)
The probability for the 2nd point: 0.4^6+0.6^5=0.00409+0.0777=0.08185 (approx)
SO required probability is: 0.08185+0.057= 0.13885

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srinivasulareddy  (11 years ago)

ans:-0.4
initially we are at '0' then start step forward and backward respectively upto 11 steps.now we reach -0.4 position .i.e,this 1 step away to reach starting point.

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Vishal sharma  (7 years ago)

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