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Probability = Sea Turtle lays eggs in front of Jhon's House?

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Manager
Joined: 13 Aug 2016
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Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  23 Aug 2016, 19:55
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28% (01:38) correct 71% (01:20) wrong based on 7 sessions
John will spend the summer in one of the houses either on Surf Street or Breaker Way. Surf Street has 1 landside house and 4 beachside houses, and Breaker Way has 1 beachside house and 2 landside houses. A sea turtle randomly lays eggs in front of a beachside house on Surf Street, and another sea turtle randomly lays eggs in front of a beachside house on Breaker Way. What are the probabilities that a sea turtle lays its eggs in front of John`s house, depending on which street he lives on?

Select all that apply

A). $$\frac{4}{25}$$

B). $$\frac{1}{5}$$

C). $$\frac{4}{15}$$

D). $$\frac{1}{3}$$

E). $$\frac{17}{15}$$
[Reveal] Spoiler: OA

Last edited by Carcass on 12 Jun 2019, 10:09, edited 7 times in total.
Edited by Carcass
Manager
Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154
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Kudos [?]: 39 [0], given: 21

Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  23 Aug 2016, 21:23
We can construct a table from the information given in this question:

--------------------------------------------------------------------------------------------------------
Surf Street | Beaker Way
--------------------------------------------------------------------------------------------------------
1 Landside house (Turtle lays egg before it) | 2 Land-side houses
--------------------------------------------------------------------------------------------------------
4 Beach-house houses | 1 Beach-house house (Turtle lays egg before it)
--------------------------------------------------------------------------------------------------------

What does randomly here mean?

How can we construct a table in user interface of this community for posting a reply or creating a new post?

Last edited by yasir9909 on 24 Aug 2016, 04:36, edited 1 time in total.
Manager
Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154
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Kudos [?]: 39 [1] , given: 21

Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  24 Aug 2016, 04:35
1
KUDOS
Probability of John to live in a house before which a turtle lays eggs : Probability of John's living in Land-side house on surf Street +Probability of John living in Beach-side house on Beaker Way = P(John in Land-side house on surf Street) + P(John in Beach-side house on Beaker Way)
= (1/5)+(1/3) = 8/15

We are actually required to calculate the possible probabilities that sea turtle lays eggs in front of John's house depending upon which street he lives on.

Now suppose:

$$Pjls$$ = Probability of John living in Land-side house on surf Street
$$Pjbs$$ = Probability of John living in Beach-side house on Beaker Way
$$Ptls$$ = Probability of turtle laying egg before Land-side house on surf Street
$$Ptbs$$ = Probability of turtle laying egg before Beach-side house on Beaker Way

$$Ptej$$ = Probability of turtle laying egg before house in which John lives

$$Pjls$$ = 1/5
$$Pjbs$$ = 1/3

$$Ptej$$ = (1/5) * $$Ptls$$ + (1/3) * $$Ptbs$$

What I am able to understand is that if the turtle lays egg randomly it means the probability of each turtle laying egg before a specific house varies between 0 and 1 i.e. it either lays eggs or it does not lay egg;in other words its probability only has two values 1 or 0.

If first turtle lays egg and second does not lay egg then

$$Ptej$$ = (1/5) * 1 + (1/3) * 0 = 1/5 ... a

If 2nd turtle lays egg and first does not lay egg then

$$Ptej$$ = (1/5) * 0 + (1/3) * 1 = 1/3 ... b

Other probabilities could be

$$Ptej$$ = (1/5) * 1 + (1/3) * 1 = 8/15
$$Ptej$$ = (1/5) * 0 + (1/3) * 0 = 0

Since Equations (a) and (b) give answer choices that give us answer choices from given list so these are the required answers

Could anybody endorse the solution to this question that I have calculated?

I have edited this post to provide a complete solution
Manager
Joined: 13 Aug 2016
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GRE 1: Q158 V154
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Kudos [?]: 39 [0], given: 21

Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  28 Aug 2016, 20:55
Dear Mr. Brent and Sandy please endorse or rectify the solution to this question so that concepts may be cleared
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Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  07 Apr 2018, 09:26
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KUDOS
The probability of John spending the summer in Surf Street = 1/2
The probability of John spending the summer in Beaker Way = 1/2

The probability a sea turtle lays eggs in front of John's house in Surf Street = 1/5 * 1/2 = 1/10
The probability a sea turtle lays eggs in front of John's house in Beaker Way= 1/3 * 1/ 2 = 1/6

The probability a sea turtle lays eggs in front of John's house is the sum of the above = 16/60 or 4/15

Manager
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Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  12 Jun 2019, 05:46
need elaboration pls
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Re: Probability = Sea Turtle lays eggs in front of Jhon's House? [#permalink]  12 Jun 2019, 10:12
Expert's post
Living in S Street is where people choose one in five houses. Turtles choose one in four houses. There are four cases in which they correspond.

So $$\frac{4}{(5*4)}=\frac{1}{5}$$
Stay at B Street, choose one of the three houses, and the turtle has only one choice.

So $$\frac{1}{(1*3)}=\frac{1}{3}$$
_________________
Re: Probability = Sea Turtle lays eggs in front of Jhon's House?   [#permalink] 12 Jun 2019, 10:12
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