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08 Mar 2019, 07:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
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58% (02:12) correct
42%
(02:17)
wrong
based on 136
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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%
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%
08 Mar 2019, 09:49
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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.
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.
08 Mar 2019, 11:05
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fskilnik
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.
