Question

A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must

fire in order to have 50% chance of hitting at least once is -

• A. 7
• B. 8
• C. 9
• D. 6

Answer 1

Answer: (A)

7

Answer 2

P(Hit) = $\frac { 1 } { 10 }$ = p ; P( $\overline { \mathrm { Hit } }$ ) = $\frac { 9 } { 10 }$ = q

P(at least 1 time hit) ³ $\frac { 1 } { 2 }$ (50 %)

1 – P (No hit) ³ $\frac { 1 } { 2 }$Ž 1– ⁿC₀$\frac { 1 } { 2 }$

$\frac { 1 } { 2 }$ ³ Ž n = 7, 8, 9.......... Ž n = (min.) = 7