If the raining season in Jerusalem begins, Dora estimates a

[fskilnik@GMATH]

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%

Answer: [spoiler]____(C)__[/spoiler]

[fskilnik@GMATH]

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%

$$? = P\left( {{\rm{Dora}}\,\,{\rm{travels}}} \right)$$
$$P\left( {{\rm{season}}\,\,{\rm{raining}}} \right) = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,P\left( {{\rm{not}}\,\,{\rm{season}}\,\,{\rm{raining}}} \right) = 30\% $$
$$20\% \,\,\mathop \to \limits^{\, + \,250\% } \,\,\,\underbrace {60\% + 10\% }_{300\% \,\left( {20\% } \right)\, + \,50\% \left( {20\% } \right)} = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
P\left( {{\rm{travel}}\,\,{\rm{when}}\,\,{\rm{season}}\,\,{\rm{raining}}} \right) = 20\% \hfill \cr
P\left( {{\rm{travel}}\,\,{\rm{when}}\,\,{\rm{not \,\, season}}\,\,{\rm{raining}}} \right) = 70\% \hfill \cr} \right.\,\,$$

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

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

Regards,
Fabio.