# How to calculate a probability based on a known probability

please, if anyone can help me.

I need to know if this statement has a solution and how. I will start to study probability and statistics, but I need to solve this now.

If the probability of a person of using their fitbit device every day for 21 days is 0.802, what is the probability of using it every day for 31 days?

• Hint: what is the probability of it happening in any one day? What do you have to assume in order to say that?
– Dave
Aug 5, 2021 at 0:07
• Dave's leading you on the right track. Just off the claim about 21 days, you can't make a claim about 31 days, unless you make certain assumptions about how usage on each day is related. Aug 5, 2021 at 0:20
• Thanks for your reply Dave and Arya. My assumption goes as follows: if my sample is 21 days, and the person use the device every single, I think of it like 100% success, and if the result is 0.802, I would say that the probability of using it on any day is 0.802. For that, I could assume that no matters if now I have a sample of 31 days, the result will be always 0.802. But I need to see this resolution in a more mathematical way. Aug 5, 2021 at 0:57
• You need to make some assumptions. If you can assume independence and constant daily probability, you have a simple basis to construct an answer. Aug 5, 2021 at 3:48
• yes! thank you @Dave for your help. Thank you Arya and Glen. I will go back to my books immediately. Aug 5, 2021 at 13:15

If we assume independence we can apply the multiplication rule ($$P(AB) = P(A)P(B)$$), and if we assume constant probability $$p$$ across days, we have $$P(\text{wear all 31 days}) = p^{31}$$ where $$p^{21}=0.802$$, or $$0.802^{(31/21)}$$.