Question

5. The probability that an archer hits the target when it is windy is 0.4, and when i is not windy the probability of a hit is 0.7. On any shot, the probability of a gust of wind is 0.3. Find the yarolalvility (a) the target is hit with a shot. (b) there was no gust of wind, assuming the target was missed.

Answer 1

P( Hits when windy ) = 0.4

P( Hits when not windy ) = 0.7

P( Windy ) = 0.3

P( Not windy ) = 1 - P( Windy )

P( Not windy ) = 0.7

a) Target hits with a shot

=> P( Hits when windy ) * P( Windy ) + P( Hits when not windy )*P( Not windy )

=> 0.4*0.3 + 0.7*0.7

= 0.12 + 0.49

= 0.61

b) No gust of wind, assuming target was missed

P( No wind | Target missed ) = ?

P (Target missed ) = 1 - P ( Target hits a shot )

= 1 - 0.61

= 0.39

P( No wind and Target missed ) = {1-P( Hits when not windy )}* P( Not windy )

= 0.3 * 0.7

= 0.21

P( No wind | Target missed ) = P( No wind and Target missed ) / P (Target missed )

= 0.21/0.39

=0.54