Probability question. Pretty tough. You think you're smart enough?

Question

There two routes up a mountain. Going up the north route, you've got an 80% chance of making it succesfully. Going up the South, you've got a 70% chance. 75% of ppl take the north, and 25% take the south. What's the prob. that a climber makes it to the top regardless of what route? And what's the prob. that a climber takes the north route and successfully reaches the top? Two climbers make it to the top to find someone already there. What's the prob. that this person used the more difficult south route?

Answer 1

A) 0.75 * 0.80 + 0.25 * 0.70 = 0.775 or 77.5 %

B) 0.75 * 0.80 = 0.60 or 60 %

C) P(South | Top) = P(South) P(Top | South) / P(Top) = (0.25 * 0.70) / 0.775 = 0.225 806 451 612 9... or approx. 22.58%

Answer 2

Total Probability for anyone to reach summit:
.75 x .80 (north route) + .25x.70 (south)=0.60 +0.175=0.775
or 77.5 %
someone taking north route and reach summit =60%
if already on top the chance shoule be 1/2 or 50% that he took South route. Once on top the chances are equal for both routes.

Answer 3

the possibility of having a green one is 5/13 and the possibility getting a black one is 8/13 so via multiplying the two you get a 40/169 probability. My answer hence is C. i don't be attentive to if that's spectacular however....

Answer 4

no clu