Question

The probability that an archer hits the target when it is windy is 0.4; when it is not windy, her probability of hitting the target is 0.7. On any shot, the probability of a gust of wind is 0.3. If the probability that She hits the target exactly once in two shots is $0.4x58$. Find the value of $x$.

Answer 1

The man will be one step away from the starting point, is

1) either he is one step ahead or

2) one step behind the starting point.

The man will be one step ahead at the end of eleven steps, is he move six steps forward and five steps backward. The probability of this event is ${}^{11}{C}_6{\left(0.4\right)}^6{\left(0.6\right)}^5$

The man will be one step behind at the end of eleven steps, it moves six steps backwards and five steps forward. The probability of this event is ${}^{11}{C}_6{\left(0.6\right)}^6{\left(0.4\right)}^5$

Therefore required probability

${=}^{11}{C}_6{\left(0.4\right)}^6{\left(0.6\right)}^5{+}^{11}{C}_6{\left(0.6\right)}^6{\left(0.4\right)}^5{=}^{11}{C}_6{\left(0.24\right)}^5$