Question

Every night I wake up between 1 and 5 am and I glance at my digital clock to check the time. All times between those hours are equally likely.

What is the probability that the clock says 3:14, 3:15, or 3:16?

Answer 1

Between 1 and 5 am, there are 299 minutes. Keep in mind that we should not include the 1:00 am and 5:00 am minutes becuase here you wake uo between 1:00 am and 5:00 am

Given  All times between those hours are equally likely

So probability that you wake up on any minute = 1/299

Probabillity that the clock says 3:14 = 1/299

Probabillity that the clock says 3:15 = 1/299

Probabillity that the clock says 3:16 = 1/299

Probability that the clock says 3:14, 3:15, or 3:16 = 1/299 + 1/299 + 1/299

= 3/299

= 0.010033