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?

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Solution

The correct option is A
4

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.

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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?

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?