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Q.

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. The probability that she hits the target on first shot is

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a

0.45

b

0.84

c

0.76

d

0.61

answer is B.

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Detailed Solution

(2)
E₁ = there is a gust of wind $\Rightarrow P (E_{1}) = 0.3$
E₂ = there is no gust of wind $\Rightarrow P (E_{2}) = 0.7$
A : Archer hits the target
$P (A) = P (E_{1}) . P (\frac{A}{E_{1}}) + P (E_{2}) . P (\frac{A}{E_{2}})$
$P (A) = (0.3) (0.4) + (0.7) (0.7) = 0.12 + 0.49 = 0.61$

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