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# What is the probability that it will rain on each of the next 3 days i

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What is the probability that it will rain on each of the next 3 days i [#permalink]

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03 Nov 2014, 08:11
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Tough and Tricky questions: Probability.

What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period? (Assume that the probability of rain on one day is independent of the probability of rain on any other day).

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Edit: Original question is below:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Edited after Ian Stewart's comment below
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Aug 2017, 01:06, edited 1 time in total.
Edited.

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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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03 Nov 2014, 13:50
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What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

A = rain
B = no rain

What is $$P(A)*P(A)*P(A) = P(A)^3$$ ?

(1) The probability of no rain throughout the first two days is 36%.

$$P(B)*P(B) = 0,36$$ ---> $$P(B) = 0,6$$

$$P(A) = 1 - P(B) = 1 - 0.6 = 0.4$$

$$P(A)^3 = 0,4^3 = 0,064$$

SUFFICIENT

(2) The probability of rain on the third day is 40%.

$$P(A) = 0,4$$
$$P(A)^3 = 0,4^3 = 0,064$$

SUFFICIENT

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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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05 Nov 2014, 13:20
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Bunuel wrote:

Tough and Tricky questions: Probability.

What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is the same in that period?

(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Raining on any day is an independent event. Lets take the probability of raining on a single day as 1/x. Therefore probability of no rain on that day is [1-1/x] .

what is asked is if 1/x * 1/x * 1/x can be found out

[1] Probability of No rain in the first two days = 36%

i.e [1-1/x] * [1-1/x] = 36% . From this we can find [1/x]^3. Therefore sufficient.

[2] Probability of rain on third day is 40%.

1/x is 40% . Probability is same for all the days. So [1/x]^3 can be found out. Therefore sufficient.

Hence D.

-------------

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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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07 Nov 2014, 09:00
Both statements are essentially saying that the probability of rain on any given day is 40%. Since the probability that it will rain on any given day is constant, both statements are sufficient on their own.

D

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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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06 Sep 2016, 21:01
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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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13 Aug 2017, 12:53
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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13 Aug 2017, 16:27
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Expert's post
Bounce1987 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

If the probability it rains on one day is p, then the probability it does not rain on one day is 1-p. The probability it does not rain on the first two days is thus (1 - p)*(1 - p). So using Statement 1, we know:

(1 - p)^2 = 36/100

Take the square root, and 1-p = 6/10, so p = 4/10. So Statement 1 is equivalent to Statement 2 - both tell us that the probability of rain on any day is 0.4. That means the probability it rains on all three days is 0.4*0.4*0.4, so we can answer the question. So the answer is D.

I'm assuming above that the probability of rain on one day is independent of the probability of rain on any other day. You can only use the multiplication rules I used above when that's true. That's something that almost certainly is not true in real life (if it rains one day, that probably makes rain more likely the next day, which means they're not independent), so any question like this really needs to tell you the events are independent, because it's not a natural thing to assume. If you don't know the events are independent, you can't solve this. Where is the question from?
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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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14 Aug 2017, 01:07
Bounce1987 wrote:
What is the probability that it will rain on each of the next 3 days if the probability of raining on any single day is
the same in that period?
(1) The probability of no rain throughout the first two days is 36%.
(2) The probability of rain on the third day is 40%.

Merging topics. Please search before posting. Thank you.
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Re: What is the probability that it will rain on each of the next 3 days i [#permalink]

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14 Aug 2017, 01:16
Stmnt 1) P(No Rain) x P(No Rain) = 36/100

So, P(No Rain)=6/10 -> P(Rain) = 4/10

Hence P(Rain)xP(Rain)xP(Rain) = (4/10)^3

Stmnt 2) P(Rain) = 4/10

Hence P(Rain)xP(Rain)xP(Rain) = (4/10)^3

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Re: What is the probability that it will rain on each of the next 3 days i   [#permalink] 14 Aug 2017, 01:16
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