Question

Bull's-eye! Lawrence likes to shoot a bow and arrow in his free time. On any shot, he has about a $10\%$chance of hitting the bull's-eye. As a challenge one day, Lawrence decides to keep shooting until he gets a bull's-eye. Let $\mathrm{Y}=$the number of shots he takes.

Short answer

The given statement is not correct, Y cannot be stated to follow the binomial distribution.

Step-by-step solution

Given Information

The likelihood of success $\left(\mathrm{p}\right)=10\%=0.10$

According to the given question

The random variable Y satisfies the following requirements.

1. The likelihood of success, i.e., the chance of hitting the bull's eye (p), which equals 0.44, is fixed.

2. There is no set number of hits.

3. Each shot is independent of the others.

4. There are two possible outcomes: he either hits or misses the bulls' eys.

All of the binomial criteria are not met in this case.

As a result, Y cannot be stated to follow the binomial distribution.