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# If the raining season in Jerusalem begins, Dora estimates a 20% probab

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If the raining season in Jerusalem begins, Dora estimates a 20% probab  [#permalink]

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08 Mar 2019, 07:46
1
1
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:30) correct 44% (02:21) wrong based on 25 sessions

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GMATH practice exercise (Quant Class 19)

If the raining season in Jerusalem begins, Dora estimates a 20% probability of traveling to Israel next holidays. If it doesn´t, she guesses her probability of taking this trip is 250% higher. Based on these assumptions, what are Dora´s chances of traveling to Israel next holidays, if she knows there is a 70% probability for the raining season in Jerusalem to begin?

(A) 15%
(B) 29%
(C) 35%
(D) 42%
(E) 46%

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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If the raining season in Jerusalem begins, Dora estimates a 20% probab  [#permalink]

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08 Mar 2019, 09:49
2
There are two possibilities of Dora travelling
1. If it rains and she travels- p(rains) x p(travel)= 0.7 x 0.2 = 0.14
2. If it does not rain and she travels - p (doesn't rain) x p (travels when it doesn't rain)
Now, the question says that probability of travelling when it does not rain is higher by 250% means that, 250% of 20% = 0.5
therefore, probability of travelling when it doesn't rain is 0.2+0.5= 0.7
So, p (doesn't rain) x p (travels when it doesn't rain)= 0.3 (given in question) x 0.7 = 0.21
P (dora travels) = P (rains and travels) OR P (doesn't rain and travels)
= 0.14 + 0.21 = 0.35
Hope this is correct.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If the raining season in Jerusalem begins, Dora estimates a 20% probab  [#permalink]

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08 Mar 2019, 11:05
fskilnik wrote:
GMATH practice exercise (Quant Class 19)

If the raining season in Jerusalem begins, Dora estimates a 20% probability of traveling to Israel next holidays. If it doesn´t, she guesses her probability of taking this trip is 250% higher. Based on these assumptions, what are Dora´s chances of traveling to Israel next holidays, if she knows there is a 70% probability for the raining season in Jerusalem to begin?

(A) 15%
(B) 29%
(C) 35%
(D) 42%
(E) 46%
Yes, ss13ny , your solution is correct! Thanks for joining!

The official solution follows:

$$? = P\left( {{\rm{Dora}}\,\,{\rm{travels}}} \right)$$

$$P\left( {{\text{season}}\,\,{\text{raining}}} \right) = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,P\left( {{\text{not}}\,\,{\text{season}}\,\,{\text{raining}}} \right) = 30\%$$

$$20\% \,\,\mathop \to \limits^{\, + \,250\% } \,\,\,\underbrace {60\% + 10\% }_{300\% \,\left( {20\% } \right)\, + \,50\% \left( {20\% } \right)} = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ P\left( {{\rm{travel}}\,\,{\rm{when}}\,\,{\rm{season}}\,\,{\rm{raining}}} \right) = 20\% \hfill \cr P\left( {{\rm{travel}}\,\,{\rm{when}}\,\,{\rm{not \,\,season}}\,\,{\rm{raining}}} \right) = 70\% \hfill \cr} \right.\,\,$$

$$?\,\, = \,\,70\% \cdot 20\% + 30\% \cdot 70\% \,\, = \,\,\underleftrightarrow {70\% \cdot \left( {20\% + 30\% } \right)}\,\, = \,\,\frac{1}{2}\left( {70\% } \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\text{C}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: If the raining season in Jerusalem begins, Dora estimates a 20% probab   [#permalink] 08 Mar 2019, 11:05
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