Probability Question 235
Question: A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is
Options:
A) $ \frac{2^{5}{{.3}^{5}}}{5^{10}} $
B) $ 462\times {{( \frac{6}{25} )}^{5}} $
C) $ 231\times \frac{3^{5}}{5^{10}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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=\frac{2}{5} $
The probability of failure in one step $ =q=0.6=\frac{3}{5}. $
In 11 steps he will be one step away from the starting point if the numbers of successes and failures 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
$ \therefore $ The required probability $ ={{}^{11}}C_6p^{6}q^{5}+{{}^{11}}C_5p^{5}q^{6} $
$ ={{}^{11}}C_6{{( \frac{2}{5} )}^{6}}.{{( \frac{3}{5} )}^{5}}+{{}^{11}}C_5{{( \frac{2}{5} )}^{5}}.{{( \frac{3}{5} )}^{6}} $
$ =462\times {{( \frac{6}{25} )}^{5}} $
BETA
