$a$ is chosen from the set $\{1,2,3,4\}$, and $b$ is chosen from the set $\{5,6,7,8,9\}$. What is the probability that the product $ab$ is a prime number?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
$a$ is chosen from the set $\{1,2,3,4\}$, and $b$ is chosen from the set $\{5,6,7,8,9\}$. What is the probability that the product $ab$ is a prime number?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac1{10}
$a$ is chosen from the set $\{1,2,3,4\}$, and $b$ is chosen from the set $\{5,6,7,8,9\}$. What is the probability that the product $ab$ is a prime number?
train