5. The probability that an archer hits the target when it is windy is 0.4, and...

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Answer 1

Answer #1

Question 5

P(Archer hits the target when it is windy) = 0.4

Pr(Archer hits the target when it is not windy) = 0.7

Pr(wind) = 0.3

Pr(Not windy) = 1 - 0.3 = 0.7

(a) Here as per bayes theorem

Pr(Hit with a shot) = P(Archer hits the target when it is windy) * Pr(WIndy) + Pr(Archer hits the target when it is not windy) * Pr(Not windy)

= 0.4 * 0.3 + 0.7 * 0.7 = 0.61

(b) Now we know the target is missed, so it will miss in two cases first there is no wind and second it is windy

Here
Pr(Target is missed) = Pr(Missed the target when it is windy) * Pr(WIndy) + Pr(Missed the target when it is not windy) * Pr(Not windy)

= (1 - 0.4) * 0.3 + (1 - 0.7) * 0.7 = 0.39

Now as per condition probability

Pr(No gust of wind if the target is missed) = (0.3 * 0.7)/0.39 = 0.5384

Answer 2

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