Probability 5 Question 17
17. A man takes a step forward with probability 0.4 and backwards with probability 0.6 . Find the probability that at the end of eleven steps he is one step away from the starting point.
(1987, 3M)
Integer Type Question
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Answer:
Correct Answer: 17. ${ }^{11} C _6(0.24)^{5}$
Solution:
- The man will be one step away from the starting point, if
(i) either he is one step ahead or (ii) one step behind the starting point.
The man will be one step ahead at the end of eleven steps, if he moves six steps forward and five steps backward. The probability of this event is ${ }^{11} C _6(0.4)^{6}(0.6)^{5}$.
The man will be one step behind at the end of eleven steps, if he moves six steps backward and five steps forward. The probability of this event is ${ }^{11} C _6(0.6)^{6}(0.4)^{5}$. $\therefore$ Required probability
$$ ={ }^{11} C _6(0.4)^{6}(0.6)^{5}+{ }^{11} C _6(0.6)^{6}(0.4)^{5}={ }^{11} C _6(0.24)^{5} $$
