<jupyter_start><jupyter_text>Assume nothing other than that they reached the "death zone" and died $$P(Summit|Reached\, 8000m)$$<jupyter_code>death_zone = north_climbs[ (north_climbs['death']==True)]
death_zone.groupby(by=['msuccess']).count()
(33)/(33+24)<jupyter_output><empty_output><jupyter_text>$P(Summit|Reached\, 8000m) = \frac{33}{33+24} = 58\%$ Using only that we know they reached the location of the ice axe (8840m) -- it does not assume it was either the ascent or descent<jupyter_code>north_climbs[(north_climbs['death'] == True) & (north_climbs['mperhighpt'] >=8440)].groupby(by=['msuccess']).count()
(33/(16+33))<jupyter_output><empty_output><jupyter_text>$P(Summit|Reached\, 8440m) = \frac{33}{33+16} = 67\%$ And the theory that they died at the ice axe site on the ascent which I will calculate at the percentage of people who die on the ascent between 8000 and 8500 meters<jupyter_code>ascent_below_first_step = north_climbs[(north_climbs['death'] == True) & (north_climbs['mperhighpt'] <= 8500 ) & (north_climbs['mperhighpt'] == north_climbs['deathhgtm'])]
ascent_below_first_step.groupby(by=['mperhighpt']).count()  # we really just need the total count, but this will break out where they died<jupyter_output><empty_output><jupyter_text>A total of 9 people out of 2835 climbs died on the ascent below the First Step Next we look at death on descent after having reached at least the ice axe location<jupyter_code>death_on_descent = north_climbs[(north_climbs['death'] == True)  & (north_climbs['mperhighpt'] >=8440) & (north_climbs['mperhighpt'] > north_climbs['deathhgtm'])]
death_on_descent.groupby(by=['msuccess']).count()
33/(33+11)<jupyter_output><empty_output><jupyter_text>$P(Summit|Died\,on\,Descent) = \frac{35}{35+14} = 75\%$<jupyter_code># Lets look at people who turn around between the Second and Third Steps
turn_around_between_second_third = north_climbs[(north_climbs['mperhighpt']>=8600) &(north_climbs['mperhighpt']<=8650)]
turn_around_between_second_third.groupby(by=['death']).count()
# for the 149 climbers who turned around after reaching the Third Step, lets look at the results
# Note 1 person died above the third step on the ascent -- that is why it does not match the 150 above


third_step_turn_around = north_climbs[(north_climbs['mperhighpt']>=8650) & (north_climbs['msuccess']==False) & (north_climbs['mperhighpt'] > north_climbs['deathhgtm'])]
third_step_turn_around.groupby(by=['death']).count()
# died on ascent above Third Step
north_climbs[(north_climbs['mperhighpt']>=8650) & (north_climbs['msuccess']==False) & (north_climbs['mperhighpt'] == north_climbs['deathhgtm'])]<jupyter_output><empty_output><jupyter_text>Now compute$$P(Summit|Reached\,Third\,Step\,and\,died\,on\,descent) $$<jupyter_code>at_least_third_step = north_climbs[(north_climbs['mperhighpt']>=8650) & (north_climbs['death']==True) & (north_climbs['mperhighpt'] > north_climbs['deathhgtm'])]
at_least_third_step.groupby(by=['msuccess']).count()
33/(33+5)<jupyter_output><empty_output><jupyter_text>$P(Summit|Reached\,Third\,Step\,and\,died\,on\,descent)  = \frac{33}{33+5} = 87\%$<jupyter_code># verify that including 'hired' does not meaningful chance the results.
# I leave out the hired because their deaths are largely due to the clients mistakes, 
# they carry much larger loads, and use much less oxygen.
# All of their names are listed at the end of this analysis
at_least_third_step_h = north_climbs_h[(north_climbs_h['mperhighpt']>=8650) & (north_climbs_h['death']==True) & (north_climbs_h['mperhighpt'] > north_climbs_h['deathhgtm'])]
at_least_third_step_h.groupby(by=['msuccess']).count()
# Review the people who died on the descent to check accuracy
# note, this database does not credit <NAME> has having reached the summit
north_climbs[(north_climbs['mperhighpt']>=8650) & (north_climbs['death']==True)]
# High point probably not accurate, so, the probability would increase slightly if he was credited with a summit.
north_climbs[(north_climbs['lname']=='Sharp') & (north_climbs['death']==True)]
# And if Sharp made the summit
34/(34+4)
# And the hero's roster
north_climbs_h[(north_climbs_h['mperhighpt']>=8000) & (north_climbs_h['death']==True) & (north_climbs_h['hired']==True)]<jupyter_output><empty_output>
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