Lying Watch

Hayley's watch displays digital time with only the hour and minute value (so 10:00:02 and 10:00:47 are all represented by 10:00 on her watch). She sees her watch read 10:00 am, runs a lap around a field and sees that her watch now reads 10:02 am. If Hayley aims to complete a lap around the field in 2 minutes or less, the probability that her time, to the nearest second, is 2 minutes or less can be expressed as $\frac {a}{b}$ , where $a$ and $b$ are positive coprime integers. What is the value of $a+b$ ?