Question

A marksman is equally likely to hit or miss his target. How many times must he fire to have a $90\%$ chance to hit the target at least once? [4 MARKS]

Answer 1

Process : 2 Marks
Calculation : 1 Mark
Result : 1 Mark

Probability of hitting = Probability of missing = $\frac{1}{2}$
“Hitting at least once” is complementary to the event “Missing every shot”.
So to have a $90\%$ chance of hitting at least once, we must ensure that:
The probability of missing every shot is less than $10\%$.
For one shot, this value is $50\%$.
For two, it is $25\%$.
For three, it is $12.5\%$.
And for four, it is $6.25\%$.
Hence, the required answer is four times.