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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?

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    $\begingroup$ Hint: what is the probability of it happening in any one day? What do you have to assume in order to say that? $\endgroup$
    – Dave
    Aug 5, 2021 at 0:07
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    $\begingroup$ 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. $\endgroup$ Aug 5, 2021 at 0:20
  • $\begingroup$ 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. $\endgroup$
    – Nahuel
    Aug 5, 2021 at 0:57
  • $\begingroup$ You need to make some assumptions. If you can assume independence and constant daily probability, you have a simple basis to construct an answer. $\endgroup$
    – Glen_b
    Aug 5, 2021 at 3:48
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    $\begingroup$ yes! thank you @Dave for your help. Thank you Arya and Glen. I will go back to my books immediately. $\endgroup$
    – Nahuel
    Aug 5, 2021 at 13:15

1 Answer 1

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The OP has got to the result with a little guidance from Dave, but for completeness, here's the result.

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 $0.802^{(31/21)}$.

However, this is for a specific 31 days. If you were looking at a person for several months, the chance that there was some period of 31 days would be much higher.

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  • $\begingroup$ Thank you @Glen_b for the clean explanation. You had been so helpful. Thank you. $\endgroup$
    – Nahuel
    Aug 7, 2021 at 13:32

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