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Question : Probability it will rain of a given day = 0.2. Calculate that probability that it will not rain for 2 days consecutively.

Solution :
$1 - 0.2 = 0.8$ (Prob. it will not rain on a give day)
$0.8 \times 0.8 = 0.64$ (Prob. it will not rain for 2 days consecutive days)

But, Why can't I do it like this :

$0.2 \times 0.2 = 0.04$ (Prob. it will rain on 2 consecutive days)
$1-(0.04)=0.96$ (Prob. it will not rain on 2 consecutive days):->Doubt

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    $\begingroup$ The first solution gives the probability that it won't rain on either day. The second solution gives the probability that it won't rain on both days. To be frank, the question is ambiguous as currently worded. Either solution could be correct for some reasonable interpretation. $\endgroup$
    – Brian Tung
    Commented Sep 7, 2022 at 20:27

1 Answer 1

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R - rain, NR - not rain

0.64 gives you NR,NR

0.96 gives you NR,NR or R,NR or NR,R

For your problem the correct answer is 0.96, since 0.64 doesn't give you the probability that it will not rain for 2 days consecutive, it gives you the probability that there will be no rain at all.

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  • $\begingroup$ Thanks for clearing it up! $\endgroup$ Commented Sep 7, 2022 at 20:25
  • $\begingroup$ You're welcome! $\endgroup$
    – eMathHelp
    Commented Sep 7, 2022 at 20:26

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