Question

Gun 1 and Gun 2 are shooting at the same target. Gun 1 shoots on the average nine shots during the same time Gun 2 shoots 10 shots. The precision of these two guns is not the same. On the average, out of 10 shots from Gun 2 seven hit the target. In the course of shooting the target has been hit by a bullet, but it is not known which Gunshot this bullet. Find the chance that the target was hit by Gun 2?

Answer 1

Let the events be defined as follows:

B = Event of hitting the target

E₁ = Event of Gun 1 hit the target

E₂ = Event of Gun 2 hit the target

Given P(E₁) = `9/(9 + 10) = 9/19`

P(E₂) = `10/(9 + 10) = 10/19`

P`("B"/"E"_1) = 12/19` ........`[∵ 1 - 7/19 = 12/19]`

P`("B"/"E"_2) = 7/19`

∴ `"P"("E"_2/"B") = ("P"("E"_2) xx "P"("B"/"E"_2))/("P"("E"_1) xx "P"("B"/"E"_1) + "P"("E"_2) xx "P"("B"/"E"_2))`

= `(10/19 xx 7/19)/(9/19 xx 12/19 + 10/19 xx 7/19)`

= `70/(108 + 70)`

= `70/178`

= 0.393